In Exercises 105–108, evaluate each expression without using a ca...

Question

In Exercises 105–108, evaluate each expression without using a calculator. log2 (log3 81)

Accepted Answer

evaluate the following log expression log base two of log base 2 to 56. Let's get started. So Let's first evaluate log 2 - 56. Log 2 - 56. Now we can rewrite this as an exponential form. Let's set this equal to Y. Our exponential form. If we have log base B. X equals Y. Is the same thing as saying the race of the Y equals X. So if you go back to our problem we can rewrite this with our base too. Race to the y equals to 56. That one figured out what number We can use from base to gonna raise face to some number to equal to 56. Do you know why? Let's say we have base to raise the some number. This number is actually eight to to the eight equals to 56. Since we have the same base. Now base two spring down her Y. And R. Eight. Other words Y equals eight. So this will be substituted back in our lock Log Base two. Alright that's in blue. Now we have log face to Of Y. Which is eight. Now we can do the same thing here. Our exponential form will be to race to the Y equals eight. We have to to the Y equals to to some number to equal eight. You could say this number is three 2 to the 3rd Power eight. Now we have the same base so we just have Y equals three. So our final answer. It's just three which is answer C. Okay I hope to help you solve the problem. Thank you for watching Goodbye.

In Exercises 105–108, evaluate each expression without using a calculator. log2 (log3 81)

Key Concepts

Logarithms

Change of Base Formula

Evaluating Logarithmic Expressions

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