Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 473: 43



Work Step by Step

Recall the quotient property of logarithms (pg. 462): $\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$ Applying this property, we get: $\log\frac{5}{2x}=1$ Now, recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation (with $b=10, y=1, x=5/2x$), we get: $10^{1}=\frac{5}{2x}$ $10(2x)=5$ $2x=\frac{5}{10}$ $2x=\frac{1}{2}$ $x=\frac{1}{4}=0.25$ We confirm that the answer works: $\log 5-\log{(2\cdot0.25)}=1$ $\log 5-\log 0.5=1$ $\log{\frac{5}{0.5}}=1$ $\log{10}=1$ $1=1$
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