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

Question

In Exercises 105–108, evaluate each expression without using a calculator. log5 (log2 32)

Accepted Answer

Evaluate the following expression, Log four of Log Base 3 81. Let's go ahead and evaluate this. The first one to find what log base 381 is Log Base 3 81. Now we can rewrite a log as an essential form. Let's first set this equal to Y. If we have a log base B of X equal to Y. This can be written as base B. Race to the Y equals X. So if you look here log base 3 81 Our base is three. Race to the Y. Equalling 81. Now you want to have the same base on both sides to find white. You have three to the y equals three to some number three raised to what number will equal 81 is the question. Well Let's say we have three races power three times 89 times three is 27 times three is 81. This number is actually four Meaning Why is equal to four. Now that we know why it's still before we can rewrite this back in our luck. Now we have log base four rivals 4 or just four. This is also for race to the first power. Imagine there's a one there. Now we can rewrite this with a different form. If we have a log in the form B. Base B raise the power of X. The base of the log in The basics are the same. Our answer is just X. Since we have log base four of the exponential force the first our X is just equal to what we can't simplify any further which means the answer to our problem is the answer. Okay. I hope to help you solve about thank you for watching. Goodbye.

In Exercises 105–108, evaluate each expression without using a calculator. log5 (log2 32)

Key Concepts

Logarithms

Change of Base Formula

Properties of Logarithms

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