## Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole

# Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 352: 42

#### Answer

a.) $x = 10$ b.) $x = 5$

#### Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_x 1000 = 3$ b.) $\log_x 25 = 2$ a.) $\log_x 1000 = 3$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 1000 = 3 \rightarrow x^3 = 1000$$ Rewrite 1000 as $10^3$ [Note: $10^3 = 10\times10\times10 = 1000$] $$x^3 = 10^3$$ $$x = 10$$ b.) $\log_x 25 = 2$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $$\log_x 25 = 2 \rightarrow x^2 = 25$$ Rewrite 25 as $5^2$ [Note: $5^2 = 5\times5 = 25$] $$x^2 = 5^2$$ $$x = 5$$

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