Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises: 55

Answer

$x=\dfrac{4}{3}+\dfrac{\log15}{3\log3}\approx2.15$

Work Step by Step

$3^{3x-4}=15$ Apply $\log$ to both sides of the equation: $\log3^{3x-4}=\log15$ Take the exponent on the left side of the equation down to multiply in front of its respective $\log$: $(3x-4)\log3=\log15$ Take $\log3$ to divide the right side: $3x-4=\dfrac{\log15}{\log3}$ Take $4$ to the right side: $3x=4+\dfrac{\log15}{\log3}$ Take $3$ to divide the right side: $x=\dfrac{4}{3}+\dfrac{\log15}{3\log3}\approx2.15$
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