https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/logarithms 2021-06-30T17:32:37Z Intro to logarithms Sal explains what logarithms are and gives a few examples of finding logarithms. Sal Khan video https://cdn.kastatic.org/googleusercontent/_RkZoOHKtmVk5F8_teMl8HJnKuYpGcFOUu9QgleddEiix-1mZsZf4T2CRlqmZLeq2jmOuybi1N6RCIMjkLHMTO8png Intro to logarithms Sal explains what logarithms are and gives a few examples of finding logarithms. https://cdn.kastatic.org/ka-youtube-converted/Z5myJ8dg_rM.mp4/Z5myJ8dg_rM.mp4 422 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/a/intro-to-logarithms 2021-06-30T17:32:36Z Intro to Logarithms Learn what logarithms are and how to evaluate them.  article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/e/logarithms_1 2021-08-05T05:39:12.794526445Z Evaluate logarithms Evaluate basic logarithmic expressions by using the fact that a^x=b is equivalent to log_a(b)=x. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/fancier-logarithm-expressions 2021-06-30T17:32:37Z Evaluating logarithms (advanced) Sal evaluates log₂(8), log₈(2), log₂(⅛), and log₈(½). Sal Khan video https://cdn.kastatic.org/googleusercontent/IFehRtPNDH5_Iynh9-56v64Afd-7uZAgvXKFmnZmB6vjo7xAyxoW4FlPVVw-Ny30g6FputZ_61JP5RZcGv-jPAl5rg Evaluating logarithms (advanced) Sal evaluates log₂(8), log₈(2), log₂(⅛), and log₈(½). https://cdn.kastatic.org/ka-youtube-converted/eTWCARmrzJ0.mp4/eTWCARmrzJ0.mp4 260 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/e/logarithms_1.5 2021-07-29T22:44:48.94944018Z Evaluate logarithms (advanced) Evaluate advanced logarithmic expressions by using the fact that a^x=b is equivalent to log_a(b)=x. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/exponential-to-logarithmic-form 2021-06-30T17:32:38Z Relationship between exponentials & logarithms Sal rewrites 100=10^2 as a logarithmic equation and log_5(1/125)=-3 as an exponential equation. Sal Khan video https://cdn.kastatic.org/googleusercontent/3vKARjWyJFh1C-eLOJYK0dOIeDgWHVLbS7WjEhBoH_Rk3x7Lp_pISiKl_0rj577hVHe7u9moxd4lNYW_2esTz7B- Relationship between exponentials & logarithms Sal rewrites 100=10^2 as a logarithmic equation and log_5(1/125)=-3 as an exponential equation. https://cdn.kastatic.org/ka-youtube-converted/Obch1OP5QyA.mp4/Obch1OP5QyA.mp4 102 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/plotting-exponential-logarithm 2021-06-30T17:32:37Z Relationship between exponentials & logarithms: graphs Given a few points on the graph of an exponential function, Sal plots the corresponding points on the graph of the corresponding logarithmic function. Sal Khan video https://cdn.kastatic.org/googleusercontent/OklmyFc2NTkPDDwTGEe3aKjrTWVBo2YqoeaoGrJ9RHRqd8jfZ4v5vWxxeb4fOIptBQTWd3MMdvtphMwpgc12Oj808A Relationship between exponentials & logarithms: graphs Given a few points on the graph of an exponential function, Sal plots the corresponding points on the graph of the corresponding logarithmic function. https://cdn.kastatic.org/ka-youtube-converted/DhW9pz5Vfwo.mp4/DhW9pz5Vfwo.mp4 250 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/logarithm-exponential-deductions 2021-06-30T17:32:41Z Relationship between exponentials & logarithms: tables Given incomplete tables of values of b^x and its corresponding inverse function, log_b(y), Sal uses the inverse relationship of the functions to fill in the missing values. Sal Khan video https://cdn.kastatic.org/googleusercontent/VNU1QaJ2ugdeCkc3zIqPQCOHZIgAKKJoNZPIrbfsqsZTaZUEeDzSaJNFlsqPKFCKecWW57AzF7DIMrsvPyoWAVzu Relationship between exponentials & logarithms: tables Given incomplete tables of values of b^x and its corresponding inverse function, log_b(y), Sal uses the inverse relationship of the functions to fill in the missing values. https://cdn.kastatic.org/ka-youtube-converted/Iz6IVf8frjw.mp4/Iz6IVf8frjw.mp4 359 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/e/understanding-logs-as-inverse-exponentials 2026-04-07T22:23:57.656416987Z Relationship between exponentials & logarithms Solve various problems that focus on the relationship between a^x=b and log_a(b)=x. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/introduction-to-logarithm-properties 2021-06-30T17:32:40Z Intro to logarithm properties (1 of 2) Sal introduces the logarithm identities for addition and subtraction of logarithms. Sal Khan video https://cdn.kastatic.org/googleusercontent/nzxy-IVnxWaW853loCOsr_TO6wouI3i0a4bHGL0q5bb_5-zRXhbax5LHz-9nuvkjyGKSZNxiidIs2_1ODvT7ocFl Intro to logarithm properties (1 of 2) Sal introduces the logarithm identities for addition and subtraction of logarithms. https://cdn.kastatic.org/ka-youtube-converted/PupNgv49_WY.mp4/PupNgv49_WY.mp4 556 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/introduction-to-logarithm-properties-part-2 2021-06-30T17:32:38Z Intro to logarithm properties (2 of 2) Sal introduces the logarithm identities for multiplication of logarithm by a constant, and the change of base rule. Sal Khan video https://cdn.kastatic.org/googleusercontent/oldCPdfzyfwKtz0lxMji9ZEt-Nau-FEnKaRQWr6BpDyEgcuA17Km-UJApBrtIFhWDW8N6ou6moT-zWtsO7Q0Jcek Intro to logarithm properties (2 of 2) Sal introduces the logarithm identities for multiplication of logarithm by a constant, and the change of base rule. https://cdn.kastatic.org/ka-youtube-converted/TMmxKZaCqe0.mp4/TMmxKZaCqe0.mp4 604 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/properties-of-logarithms 2021-06-30T17:32:35Z Intro to logarithm properties Learn about the properties of logarithms and how to use them to rewrite logarithmic expressions. For example, expand log₂(3a). article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/sum-of-logarithms-with-same-base 2021-06-30T17:32:36Z Using the logarithmic product rule Sal rewrites log₃(27x) as log₃(27)+log_3(x), which is simplified as 3+log₃(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/5MtLeuscbvcpVcHJ0-Qt3nt1E1p_CrCCvm4UcbsVhEOzA_61CdCCHHAkRodqwHd8UISxK1_NTwC7y5fLlvGgGynO Using the logarithmic product rule Sal rewrites log₃(27x) as log₃(27)+log_3(x), which is simplified as 3+log₃(x). https://cdn.kastatic.org/ka-youtube-converted/pkGrXzakRFs.mp4/pkGrXzakRFs.mp4 304 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/logarithm-of-a-power 2021-06-30T17:32:36Z Using the logarithmic power rule Sal rewrites log₅(x³) as 3log₅(x). Sal Khan video https://cdn.kastatic.org/googleusercontent/JxsKX2I589_-eB_dH7R6UewKd_mAmWHv-oSLHZo6EM_qGogJOQscodPVmb12I-6g6Yr3xg1v8UsCL7afMtOjhSeR Using the logarithmic power rule Sal rewrites log₅(x³) as 3log₅(x). https://cdn.kastatic.org/ka-youtube-converted/Pb9V374iOas.mp4/Pb9V374iOas.mp4 289 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/e/logarithms_2 2025-12-22T06:46:20.288709789Z Use the properties of logarithms Use the properties of logarithms in order to rewrite a given expression in an equivalent, different form. Rob Yates exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/using-multiple-logarithm-properties-to-simplify 2021-06-30T17:32:36Z Using the properties of logarithms: multiple steps Sal rewrites log_5([25^x]/y) as 2x-log_5(y) by using both the log subtraction property and the log multiplied by a constant property. Sal Khan video https://cdn.kastatic.org/googleusercontent/5VlTSPMDj30LcBC1BjamB_Cu5qwPr5bN17ZobcRYp150nYz1jqNwUTFqHNaRKVrBHg3FJzcIvR_47SCrDzAHhJNC Using the properties of logarithms: multiple steps Sal rewrites log_5([25^x]/y) as 2x-log_5(y) by using both the log subtraction property and the log multiplied by a constant property. https://cdn.kastatic.org/ka-youtube-converted/RhzXX5PbsuQ.mp4/RhzXX5PbsuQ.mp4 130 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/proof-log-a-log-b-log-ab 2021-06-30T17:32:40Z Proof of the logarithm product rule Sal proves the logarithm addition property, log(a) + log(b) = log(ab). Sal Khan video https://cdn.kastatic.org/googleusercontent/qo2NMolmBgYNDjz2JPjqX6wchSU-NnH00fnY9dS_CtuQglkKD8xahn53DQdSxv_h2tKdneH2FwMec0Cw12IxuGy6ZA Proof of the logarithm product rule Sal proves the logarithm addition property, log(a) + log(b) = log(ab). https://cdn.kastatic.org/ka-youtube-converted/FP2arCfAfBY.mp4/FP2arCfAfBY.mp4 428 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/proof-a-log-b-log-b-a-log-a-log-b-log-a-b 2021-06-30T17:32:40Z Proof of the logarithm quotient and power rules Sal proves the logarithm quotient rule, log(a) - log(b) = log(a/b), and the power rule, k⋅log(a) = log(aᵏ). Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof of the logarithm quotient and power rules Sal proves the logarithm quotient rule, log(a) - log(b) = log(a/b), and the power rule, k⋅log(a) = log(aᵏ). https://cdn.kastatic.org/ka-youtube-converted/yEAxG_D1HDw.mp4/yEAxG_D1HDw.mp4 479 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/justifying-the-logarithm-properties 2021-06-30T17:32:37Z Justifying the logarithm properties Study the proofs of the logarithm properties: the product rule, the quotient rule, and the power rule. article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/v/change-of-base-formula 2021-06-30T17:32:38Z Evaluating logarithms: change of base rule Sal approximates log₅(100) by rewriting it as log(100)/log(5) using the change of base rule, then evaluates with a calculator. Sal Khan video https://cdn.kastatic.org/googleusercontent/Ox4Y33CIe_pIjlgkQxe2Q_coviHCt4pHeuaw-hle03SIpJdm0WSsNyJHQPjl1oYY-eFeyUG_6kup3RwUmVRqBTyvMQ Evaluating logarithms: change of base rule Sal approximates log₅(100) by rewriting it as log(100)/log(5) using the change of base rule, then evaluates with a calculator. https://cdn.kastatic.org/ka-youtube-converted/OkFdDqW9xxM.mp4/OkFdDqW9xxM.mp4 452 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-change-of-base-rule-intro 2021-06-30T17:32:35Z Logarithm change of base rule intro Learn how to rewrite any logarithm using logarithms with a different base. This is very useful for finding logarithms in the calculator! article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/e/evaluate-logarithms-using-the-change-of-base-rule 2025-06-26T19:19:31.08788297Z Evaluate logarithms: change of base rule Evaluate any logarithm in a calculator with the use of the change of base formula. Example: Evaluate log₅(100). Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/v/rewriting-logarithmic-expressions-change-of-base 2022-10-06T23:23:50.639907812Z Using the logarithm change of base rule Sal rewrites logarithmic expressions like 1/(logₐ4) or logₐ(16)*log₂(a) using the change of base rule. video https://cdn.kastatic.org/ka_thumbnails_cache/8a0ca8c6-17c9-42a1-9d71-3cf53b6e1fad_1280_720_base.png Using the logarithm change of base rule Sal rewrites logarithmic expressions like 1/(logₐ4) or logₐ(16)*log₂(a) using the change of base rule. https://cdn.kastatic.org/ka-youtube-converted/qtsMgdZ98Yg.mp4/qtsMgdZ98Yg.mp4 403 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/e/rewrite-logarithmic-expressions-using-the-change-of-base-rule 2025-05-05T08:14:25.350149109Z Use the logarithm change of base rule Find the logarithmic variable expression that is equivalent to a given logarithmic expression. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/v/change-of-base-formula-proof 2021-06-30T17:32:38Z Proof of the logarithm change of base rule Sal proves the logarithmic change of base rule, logₐ(b)=logₓ(b)/logₓ(a). Sal Khan video https://cdn.kastatic.org/googleusercontent/v4Cdk-AdbU_yCqsL3Zh92DTQmXQkhiwc6T3i9ZiU16GLoXyNQsda1wiUElIQ9kQM5uFFI6uzcPUEQl2LQs9PBuiJuw Proof of the logarithm change of base rule Sal proves the logarithmic change of base rule, logₐ(b)=logₓ(b)/logₓ(a). https://cdn.kastatic.org/ka-youtube-converted/1reblXFlM6I.mp4/1reblXFlM6I.mp4 299 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/a/logarithm-properties-review 2021-06-30T17:32:35Z Logarithm properties review Review the logarithm properties and how to apply them to solve problems. article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/v/exponential-equation 2021-06-30T17:32:35Z Solving exponential equations using logarithms: base-10 Sal solves the equation 10^(2t-3)=7. Sal Khan video https://cdn.kastatic.org/googleusercontent/N9ubBpdN-foPzJPD0nPnukCHjrYPQCJ-9RnJjfivA4PXs7hM5KOxrdyuujuEYDIiW8942VkoQzD_0cSF-2ofKmPW Solving exponential equations using logarithms: base-10 Sal solves the equation 10^(2t-3)=7. https://cdn.kastatic.org/ka-youtube-converted/R443Db-wJ5o.mp4/R443Db-wJ5o.mp4 171 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/a/solving-exponential-equations-with-logarithms 2021-06-30T17:32:36Z Solving exponential equations using logarithms Learn how to solve any exponential equation of the form a⋅b^(cx)=d. For example, solve 6⋅10^(2x)=48. article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/e/using-logarithms-to-solve-exponential-equations 2026-04-07T23:36:17.218592739Z Solve exponential equations using logarithms: base-10 and base-e Solve exponential equations that have 10 or e at the base of the exponential term. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/v/solve-exponentials 2021-06-30T17:32:38Z Solving exponential equations using logarithms: base-2 We can use logarithms to solve *any* exponential equation of the form a⋅bᶜˣ=d. For example, this is how you can solve 3⋅10²ˣ=7: 1. Divide by 3: 10²ˣ=7/3 2. Use the definition of logarithm: 2x=log(7/3) 3. Divide by 2: x=log(7/3)/2 Now you can use a calculator to find the solution of the equation as a rounded decimal number ​ Sal Khan video https://cdn.kastatic.org/googleusercontent/V2up2to5PR6Rd5FyS6YarI7kTmR9UVn4PizH2ue0u_k8c6zC-amA-1hidij5mGGNvxKEPuC_tG8d-XNbrHMH2-I4 Solving exponential equations using logarithms: base-2 We can use logarithms to solve *any* exponential equation of the form a⋅bᶜˣ=d. For example, this is how you can solve 3⋅10²ˣ=7: 1. Divide by 3: 10²ˣ=7/3 2. Use the definition of logarithm: 2x=log(7/3) 3. Divide by 2: x=log(7/3)/2 Now you can use a calculator to find the solution of the equation as a rounded decimal number ​ https://cdn.kastatic.org/ka-youtube-converted/7Ig6kVZaWoU.mp4/7Ig6kVZaWoU.mp4 312 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/e/solve-exponential-equations-using-logarithms-base-2 2026-04-07T23:17:37.123726494Z Solve exponential equations using logarithms: base-2 and other bases Solve exponential equations that have 2 or other numbers at the base of the exponential term. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-models/v/solving-exponential-model-word-problems-1 2022-10-06T23:23:50.639907812Z Exponential model word problem: medication dissolve Sal solves an exponential equation in order to answer a question about an exponential model. video https://cdn.kastatic.org/ka_thumbnails_cache/41225e5a-8ede-4796-b485-b4e5fcc8c844_1280_720_base.png Exponential model word problem: medication dissolve Sal solves an exponential equation in order to answer a question about an exponential model. https://cdn.kastatic.org/ka-youtube-converted/HnHCQ2X_meg.mp4/HnHCQ2X_meg.mp4 245 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-models/v/solving-exponential-model-word-problems-2 2022-10-06T23:23:50.639907812Z Exponential model word problem: bacteria growth Sal evaluates an exponential function at a specific value in order to answer a question about an exponential model. video https://cdn.kastatic.org/ka_thumbnails_cache/9797a914-e6d1-4df9-8054-945636cf3dc0_1280_720_base.png Exponential model word problem: bacteria growth Sal evaluates an exponential function at a specific value in order to answer a question about an exponential model. https://cdn.kastatic.org/ka-youtube-converted/IpXL9HIkqUQ.mp4/IpXL9HIkqUQ.mp4 94 Logaritmos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-models/e/exponential-models-word-problems 2026-04-07T22:23:57.656416987Z Exponential model word problems Solve word problems about exponential situations. Stacy Beaudoin exercise