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Chapter 4: Problem 105

Evaluate each expression without using a calculator. $$\log _{3}\left(\log _{7} 7\right)$$

Short Answer

Expert verified
The value of \(\log_{3}\left(\log_{7} 7\right)\) is 0.

Step by step solution

01

Simplifying the Inner Logarithm

First, let's simplify the inner logarithm - the \(\log_{7}{7}\). From the basic property of logarithms, we know that the logarithm of a number with the same number as its base equals to 1. So, the \(\log_{7}{7}\) simplifies to 1.
02

Simplifying the Outer Logarithm

Now we are left with \(\log_{3}{1}\). Again, it's a known fact that the logarithm of 1 in any base is 0. It simplifies to 0 in this case as well.

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Most popular questions from this chapter

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