/*! 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 33 Evaluate each expression without... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 33

Evaluate each expression without using a calculator. $$\log _{64} 8$$

Short Answer

Expert verified
The value of \( \log_{64} 8\) is \(\frac{1}{2}\)

Step by step solution

01

Simplify the Bases

First, simplify the bases of 64 and 8 as they are both powers of 2. This transforms the expression into: \(\log_{2^6}(2^3)\)
02

Simplify Logarithm

Now apply the power rule of logarithms which brings down the exponent to the front. The expression becomes: \(\frac{1}{6} \log_{2}(2^3)\)
03

Simplify the Logarithm to Its Base

The base of the log and the number under the log are the same (both 2), so the expression simplifies to: \(\frac{1}{6} * 3 = \frac{1}{2}\)

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