Precalculus (6th Edition) Blitzer

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

Chapter 3 - Test - Page 515: 17

Answer

$ x= 5$

Work Step by Step

We are given that $\log x+\log (x+15)=2$ Use rule: $\log_b{p \cdot q} =\log p + \log q $ $\log [ x(x+15)]=100$ or, $ x^2+15 x-100 =0$ or, $(x-5)(x+20)=0$ Simplify it by equating both factors to $0$: $ x -5 =0 \implies x =5$ and $ x +20 =0 \implies x=-20$ But negative values cannot be considered (because we can not take the log of a negative number). So, the result is: $ x= 5$
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