If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:5:59

Relationship between exponentials & logarithms: tables

CCSS.Math:

Video transcript

we've got two tables over here this first table tells us that for any given value of x what is the value of B to the X so for example if we look right over here with X is one point five eight five B to the one point five eight five is three so this this is telling us that B to the one point five eight five is equal to three similarly similarly I can never say that it's telling us that B to the two point three two two is five be the two point eight oh seven to seven B to the two point one six nine is nine now this table over here is telling us for any given value of y what is going to be log base B of Y so this tells us that log base B of A is zero log base B of 2 is one log base B of 2 C is one point five eight five log base B of 10 D so this is literally this is telling us that log base B of 10 D is equal to two point three to two that's what this last column tells us now what I challenge you to do is pause this video and using just the information here and you don't need a calculator in fact you can't use a calculator I forbid you try to figure out try to figure out what a B C and D are just using your powers of reasoning no calculator involved just use your powers of reasoning can you figure out what a B C and D are so I'm assuming you've given a go at it so let's see what we can do from this so here we have just a bunch of numbers we we need to figure out what B is so and these are all kind of you know B to the 1.58 five power is three I don't really know what to make sense of this stuff here maybe maybe this table will help us so this first let me do this in different colors this first column right over here tells us that log base B of a so now Y is equal to a that that is equal to zero now this is an equivalent statement to saying that B to the a power is equal to is a sign not be to the a power this is an equivalence a statement to saying be to the zero power to the zero power is equal to a this is saying what exponent do I need to raise B to to get a well you raise it to the zero power this is saying B to the zero power is equal to a now what is anything to the 0 power assuming that it's not zero if we're assuming that we're dealing with that B is not zero if we're assuming that B is not zero then so we're going to assume that and we can't assume and I think that's a safe assumption because we're raising beat all of these other powers we're getting a nonzero value so since we know that B is not zero anything that the zero power is going to be one so this tells us that a is equal to one so that's we got one figured out a is equal to one now let's look now let's look at this next piece of information right over here what does that tell us that tells us that log base B of 2 of 2 is equal to 1 this is a equivalent to saying the power that I need to raise B to to get to 2 is 1 or if I want to write an exponential form I could write this is saying that B to the first power is equal to 2 so I'm raising something to the first power and I'm getting 2 what is this thing well that means that B must be 2 2 to the first power is 2 so b is equal B is B is equal to 2 B to the first power is equal to you could say B to the first is equal to 2 to the first that's also equal to 2 so B must be equal to 2 so we've been able to figure that out so this is a 2 right over here it actually makes sense two to the one point five eight five power that yeah that feels right that that's about three now let's see what else we can do let's see if we can figure out C so let's look at this column let's see what this column is telling us that column we could read it as log base B now our Y is 2 C log base B of 2 C is equal to one point five eight five or we could read this as be if we write an exponential form B to the 1.58 5 is equal to 2c now what's B to the one point five eight five well they tell us right over here that B to the one point five eight five is three is three so this right over here is equal to three so we get to C is equal to three or divide both sides by two we would get C is equal to one point five this is working out pretty well and now we have this last column which I will circle in purple and we can re we can write this as log base B of ten D of 10 D is equal to two point three to two so this is saying the power I need to raise B to to get to ten D is two point three to two or in exponential form B to the 2 point 3 to 2 is equal to 10 D now what is B to the two point three to two well they tell us over here B B to the 2 point 3 to 2 is 5 so this is equal to 5 so we could write 10 D is equal to 5 or divide both sides by 10 D is equal to 0.5 and we're done we were able to figure out what a B and C a B C and D are without the use of a calculator