/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 769 Evaluate \(\left(\log _{10} 12\r... [FREE SOLUTION] | 91影视

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Chapter 26: Problem 769

Evaluate \(\left(\log _{10} 12\right) /\left(\log _{10} 5\right)\).

Short Answer

Expert verified
The final answer is \(\frac{\log_{10}(12)}{\log_{10}(5)}\).

Step by step solution

01

Understand the problem

We are given a logarithm quotient: \(\frac{\log_{10}(12)}{\log_{10}(5)}\). Our goal is to first evaluate each logarithm and then divide the results.
02

Evaluate the logarithms

Evaluate each logarithm separately: 1. \(\log_{10}(12)\) means "what power do we need to raise 10 to in order to get 12?" We can't directly find the exact value in terms of integers, so we will keep the notation as such. 2. \(\log_{10}(5)\) similarly means "what power do we need to raise 10 to in order to get 5?" Again, the exact value in terms of integers cannot be directly found, so we keep the notation as such. Therefore, we have \(\frac{\log_{10}(12)}{\log_{10}(5)} = \frac{\log_{10}(12)}{\log_{10}(5)}\).
03

Divide the results

Since we cannot simplify the logarithms further, we can leave the expression as it is: \(\frac{\log_{10}(12)}{\log_{10}(5)}\). This is the final answer.

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