Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 35

Answer

a.) x = 64 b.) x = -2

Work Step by Step

$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$ a.) $\log_4 x = 3$ b.) $\log_{10} 0.01 = x$ a.) $\log_4 x = 3$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $\log_4 x = 3 \rightarrow 4^3 = x$ $x = 4^3$ $x = 64$ b.) $\log_{10} 0.01 = x$ Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$ $\log_{10} 0.01 = x \rightarrow 10^x = 0.01$ [When turning 0.01 into a fraction, we get $\frac{1}{100}$, which happens to expand to be $\frac{1}{10\times10}$. We can convert it then to $10^{-2}$] $10^x = 10^{-2}$ $x = -2$
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