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Proof of the logarithm product rule

Sal proves the logarithm addition property, log(a) + log(b) = log(ab). Created by Sal Khan.

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• Either I ams tupid, or Sal is just using the rule as its own proof.

It's like saying 2+2=4, and since 2+2=4, we can deduct 4=2+2, thus 2+2=4.

• It's almost like you say, because it's so simple that the proof seems unnecessary:

Since you add exponents of powers of the same base to get the exponent of the product, and since logs are exponents, the log_b of the product is the sum of the logs_b of the factors.
(1 vote)
• Though it has not been mentioned in the video , what are anti-logarithms?
• An anti-logarithm is essentially exponentiation. For example:

log (base 10) 5 = .6989700043
10^.6989700043 = 5
• At around , you say that x^l * x^m = x^(l+m)
I thought it would be 2x^(l+m)

WHat am I missing?
• Where would you get the 2 from? You are multiplying, not adding.
Try this with some actual number, maybe that might make the concept more clear:
4² * 4³ = 4*4 * 4*4*4 = 4⁵ = 1024
• Feels like he did this one on an etch a sketch. Can't read any of that ;-x
• Did Sal really refer to his colors 6 times in a single video?
• how is this concept useful guys somebody help?
• In science and engineering, there are a lot of phenomena that are exponential in nature. The variables are in the exponent, not in the base. In order to solve for the variables you have to take the log of the exponential functions. This is actually used a lot.
• Why is the video so blurry?
Pls make another one
• if you had the equation 4^x-2=15^-2x , how could you solve for x so that you would get the exact answer using base 10 logarithms? please help me using this example I cannot wrap my head around it! Thank you!