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

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 $\frac{1}{49}$ .

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

Short Answer

Step by step solution

Step 1. Convert into exponential form

Step 2. Check the solution

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In the following exercises, solve for x.log7x=-2

Short Answer

Step by step solution

Step 1. Convert into exponential form

Step 2. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

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