Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 488: 40


$x \approx -10.25$

Work Step by Step

The base in the exponential equation is $3$, so take the natural logarithm on both sides to obtain $\ln{(3^{\frac{x}{7}})}=\ln{0.2}.$ Use the power rule $\ln{a^x}=x\ln{a}$ to bring down the exponent: $(\frac{x}{7})\ln{3} = \ln{0.2}.$ Divide both sides by $\ln{3}$ to obtain $\dfrac{x}{7} = \dfrac{\ln{0.2}}{\ln{3}}.$ Multiply both sides by $7$ to obtain $x = 7 \cdot \dfrac{\ln{0.2}}{\ln{3}}.$ Use a calculator and round-off the answer to two decimal places to obtain $x \approx -10.25.$
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