In Exercises 21–42, evaluate each expression without using a calc...

Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 64

Accepted Answer

Hey everyone welcome back in this problem. We are asked to evaluate the following expression. Were given log base three of 81. Now, reading what we're given log base three of 81. Let's go ahead. Set that equal to why? Okay so why is going to be what we're trying to find? The evaluation of that expression. Alright now let's recall our log rules. We know that if we have log base B of some quantity X equal to y. Just like in our case we can rewrite this as B to the exponent Y equals X. Okay so be the base of the log rhythm becomes the base of the exponent. Alright so applying this to our expression, we have the base of the log rhythm is three. So in our case B is going to be three so we can write three. Okay why is the same in both of these? We're gonna have three to the y. Is going to be equal to 81. Okay. The value or whatever is inside of that log rhythm. Alright so now we have an equation three to the exponent Y is equal to 81. When we have an equation like this, what we want to do is we want to try to get the same base on both sides that will allow us to compare the exponents. Okay so we have three to the Y. On the left hand side. Well we know we can write three, the exponent four is equal to 81. Okay, 81 is gonna be equal to three to exponent four. Okay now and if you didn't recall that, what you can do is you can do a little table so we know we want base three. So we do the exponent and the result oops. And the result is going to be three to the exponent. So if we do a little table we have exponent one, we get three. We have the exponent two. We know three times three is gonna be nine. Okay, so each time we're multiplying by three we have the exponent three. Well we multiply by three again we get 27 then in the exponent four we multiply by three again and we get 81. Okay? So if you're having a hard time remembering all of the exponents, if you're in a test and you're not sure. You can always do A little table like this and then you just have to worry about multiplying by three. Multiplying by three. Okay. And it can be a little bit simpler of of a way to build up that exponent. Um if you don't have a calculator. All right, so we have three to the y is equal to 3 to 4. Well we have two things that are equal the bases are equal. That means the exponents must be equal. So we must have y equals four. Okay. And why is the quantity we were looking for? So there we go. Our answer is four. That's going to be be I hope this video helped. Thanks for watching.

In Exercises 21–42, evaluate each expression without using a calculator. log2 64

Key Concepts

Logarithms

Base of a Logarithm

Exponential Form

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