Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises: 24

Answer

$$y=9$$

Work Step by Step

$\log_3y+3\log_3{y^2}=14$ Expressing the left side as the base-3 log of a single expression: $\log_3({y\times ({y^2})^3)}=14$ Simplifying the left side: $\log_3 {y^7}=14$ Raising 3 to both sides of the equation: $y^7=3^{14}$ Solving for $y$: $y=({3^{14}})^{\frac{1}{7}}=3^2=9$
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