/*! 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 19 Evaluate each logarithm. $$ ... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 19

Evaluate each logarithm. $$ \log _{49} 7 $$

Short Answer

Expert verified
The value of \(\log _{49} 7\) is 2.

Step by step solution

01

Identify the base and number

Here, the base of the logarithm is 49 and the number is 7.
02

Express the base as power of number

Express 49 as a power of 7. It is equal to \(7^2\).
03

Apply the power rule of Logarithm

According to the power rule of logarithms, logarithm base B of A to the power of N is equal to N times logarithm base B of A. The given logarithm can be rewritten as \(\log _{7^2} 7 = 2 \cdot \log_{7} 7\)
04

Evaluate the result

Logarithm of a number to the same base equals 1 according to the identity rule of logarithms. So, \(\log_{7} 7 = 1\). Substitute this into our expression from the last step, the result will be \(2 \cdot 1\).

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