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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 398 (page 1064)

In the following exercises, solve for x.
$\log_{7} (x) = - 2$

Short Answer

Expert verified

The solution is $x = \frac{1}{49}$ .

Step by step solution

01

Step 1. Convert into exponential form

Consider the logarithm equation $\log_{7} (x) = - 2$ .

Its equivalent exponential form is given as

$\begin{array}{rcl} 7^{- 2} & = & x \\ \frac{1}{7^{2}} & = & x \\ \frac{1}{49} & = & x \end{array}$

So the solution is $\frac{1}{49}$ .

02

Step 2. Check the solution

Substitute $\frac{1}{49}$ for $x$ in the original equation.

$\begin{array}{rcl} \log_{7} (x) & = & - 2 \\ \log_{7} (\frac{1}{49}) & = & - 2 \\ 7^{- 2} & = & \frac{1}{49} \\ \frac{1}{7^{2}} & = & \frac{1}{49} \\ \frac{1}{49} & = & \frac{1}{49} \end{array}$

As the statement is true, so the found solution is correct.

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Most popular questions from this chapter

In the following exercises, solve each equation.

$4^{x + 2} = 64$

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$鈸� 2^{x} 鈸� 2^{x + 1} 鈸� 2^{x - 1} 鈸� 2^{x} + 2 鈸� 2^{x} 鈭� 2 鈸� 3^{x}$

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