Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set - Page 727: 84

Answer

$x=\frac{1}{5}$

Work Step by Step

The product rule for logarithms says that $\log_b{MN}=\log_bM+\log_bN$ i.e. the logarithm of a product is the sum of the logarithms. The quotient rule for logarithms says that $\log_b{\frac{M}{N}}=\log_bM-\log_bN$ i.e. the logarithm of a quotient is the difference of the logarithms. The power rule for logarithms says that $\log_b{M^p}=p\log_bM$ i.e. the logarithm of a number with an exponent is the exponent times the logarithm of the number. $\log_ba=\frac{\log_ca}{\log_cb}$ Hence here: $\log {(x+7)}-\log3=\log{\frac{x+7}{3}}$ We know that if $a\gt0,a\ne1$, then $\log_ab=\log_ac\longrightarrow b=c$ Thus here: $\frac{x+7}{3}=7x+1\\x+7=21x+3\\4=20x\\x=\frac{1}{5}$
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