/*! 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 4: Problem 33

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

Short Answer

Expert verified
The value of \(\log _{64} 8\) is \(0.5\)

Step by step solution

01

Identify Common Base

Rewrite \(64\) and \(8\) as \(2^6\) and \(2^3\) respectively, to identify a common base
02

Apply Change of Base Formula

Apply change of base formula with base \(2\). This transforms \(\log _{64} 8 = \log _{2^6} 2^3\) into \(\frac {\log _2 2^3} {\log _2 2^6}\)
03

Simplify Logarithm

Simplify \(\log _2 2^3\) as \(3\) and \(\log _2 2^6\) as \(6\)
04

Conclude

After simplifying, you have \(\frac {3} {6}\) which equals \(0.5\)

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Most popular questions from this chapter

What question can be asked to help evaluate \(\log _{3} 81 ?\)

Explain how to use the graph of \(f(x)=2^{x}\) to obtain the graph of \(g(x)=\log _{2} x\).

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Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$3^{x}=2 x+3$$
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