Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1: 27

Answer

$x=\frac{1}{3}\ln(\frac{7}{2})$

Work Step by Step

Divide each side of the equation by 2, leaving $e^{3x}=\frac{7}{2}$. Take the natural logarithm of each side to get $ln(e^{3x})=ln(\frac{7}{2})$, which simplifies to $3x=ln(\frac{7}{2})$ after using the log rule $\log(a^b)=b \times \log(a)$. Dividing each side by three leaves $x=\frac{1}{3}\ln(\frac{7}{2})$.
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