/*! 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 124 Solve: \(\log _{3}(x+5)=2\) (S... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 124

Solve: \(\log _{3}(x+5)=2\) (Section 3.4, Example 6)

Short Answer

Expert verified
\[x = 4\]

Step by step solution

01

Convert the logarithmic equation into an exponential equation

The base of the logarithm in the equation is 3, the logarithm of \(x+5\) equals 2. Therefore, we can convert this logarithmic equation into an exponential equation using the base 3. This gives us: \(3^2 = x+5\).
02

Simplify the exponential equation

Simplifying \(3^2 = x+5\) results in 9 = \(x+5\).
03

Solve for \(x\)

To solve for \(x\), subtract 5 from both sides of the equation. This gives us: \(x = 9 - 5\).

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Most popular questions from this chapter

Solve: \(\quad \log _{2}(2 x+1)-\log _{2}(x-2)=1\) (Section 3.4, Example 7)

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In Chapter \(5,\) we will prove the following identities: $$ \begin{aligned} \sin ^{2} x &=\frac{1}{2}-\frac{1}{2} \cos 2 x \\ \cos ^{2} x &=\frac{1}{2}+\frac{1}{2} \cos 2 x \end{aligned} $$ Use these identities to solve. Use the identity for \(\sin ^{2} x\) to graph one period of \(y=\sin ^{2} x\)

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