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

Question

In Exercises 105–108, evaluate each expression without using a calculator. log5 (log7 7)

Accepted Answer

Evaluate the following expression log base three of log fish. 1212. Let's first evaluate log base 12 of 12. What? 12? 12? one of our log rules states that if we have a luck with base of an exponential base the X. That's just equal to X. Because the bases are the same in both the log and the exponential. Well if you look here we have log base 12 of 12. The base of the log and the basic exponential are the same. I see exponential because you can imagine this is 12 to the first because the basic exponential the log is the same. We have X equals one. It's just the one there. So that evaluates to one. Now can we write log base three of one. No one evaluate this luck. Let's say this is equal to y. Log phase three of one equals Y. We can make use of the exponential form of a luck. If we have log base B of X equals Y. The essential form is given by base race. The Y equals X. So We have three reds of the wine equals one. Now the final why? We want to have the same base on both the left side and the right side of the equal sign. So let's say three to the Y equals three to some number. Now 3, 2. That number should equal one. We should know that any base raised to the power of zero or equal one. In other words three to the Y equals three to the zero. Now we have the same base we can spring down. Ry and bring down our zero. Sorry, answer should be zero, which means our answer is answer D. 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. log5 (log7 7)

Key Concepts

Logarithm Basics

Change of Base Formula

Properties of Logarithms

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