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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 458 (page 1067)

Solve forx: $\log_{5} (x) = - 3$

Short Answer

Expert verified

The required value ofxis $\frac{1}{125}$ .

Step by step solution

01

Step 1. Given information.

Consider the given equation,

$\log_{5} (x) = - 3$

Compare the given equation with the standard form $x = a^{y}$ , we get,

$y = - 3, a = 5,$

02

Step 2. Convert into exponential form.

Convert logarithmic equation into exponential equation,

$x = a^{y} x = 5^{- 3} x = \frac{1}{5^{3}} x = \frac{1}{125}$

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Most popular questions from this chapter

In the following exercise, find the inverse of each function.

$f (x) = \sqrt{x + 8}, x \geq - 8$

In the following exercises, solve each equation.

$4^{x} = 32$

In the following exercises, solve each equation.

$3^{x^{2} - 2 x} = \frac{1}{3}$

Find the inverse of the function , $f (x) = 8 x + 5$

Graph: $g (x) = {(\frac{1}{5})}^{x}$

See all solutions

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