/*! 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 14 Evaluate each logarithm. $$ ... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 14

Evaluate each logarithm. $$ \log _{2} 16 $$

Short Answer

Expert verified
\(\log _{2} 16 = 4\)

Step by step solution

01

Understand Logarithms

A logarithm is an operation that determines how many times a certain number, called the base, must be multiplied by itself to achieve another number. In the given logarithm \(\log _{2} 16\), the base is 2 and we need to find out how many times 2 must be multiplied by itself to get 16.
02

Perform Calculations

We start with 2 and keep multiplying it by itself: \[\begin{align*}2^1 &= 2, \2^2 &= 2*2 = 4,\2^3 &= 2*2*2 = 8,\2^4 &= 2*2*2*2 = 16.\end{align*}\]So, it's clear that 2 needs to be multiplied by itself 4 times to get 16.
03

Final Answer

\(\log _{2} 16 = 4\), because 2 needs to be multiplied by itself 4 times to get 16.

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Most popular questions from this chapter

The Nut Shop carries 30 different types of nuts. The shop special is the Triple Play, a made-to-order mixture of any three different types of nuts. How many different Triple Plays are possible?

Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient. $$ \log _{9} 3.3 $$

Solve each equation. If necessary, round to the nearest ten-thousandth. $$ 4 \log _{3} 2-2 \log _{3} x=1 $$

Solve each equation. Check your answers. $$ \log 6 x-3=-4 $$

Solve each equation. Check your answers. $$ 3 \log x=1.5 $$
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