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: 41

Answer

$x=\sqrt{\frac{10^{11}}{2}}\approx 223606.7977$

Work Step by Step

Recall the product property of logarithms (pg. 462): $\log_b{mn}=\log_b{m}+\log_b{n}$ Applying this property to our equation, we get: $\log (2x\cdot x)=11$ $\log{(2x^2)}=11$ Next, recall the definition of a logarithm (pg. 451): $\log_{b}{x}=y$ iff $b^y=x$ Applying this definition to our equation (with $b=10, y=11, x=2x^2$), we get: $10^{11}=2x^2$ $x^2=\dfrac{10^{11}}{2}$ $x=\sqrt{\frac{10^{11}}{2}}\approx 223606.7977$ We confirm that the answer works: $\log {\left(2\cdot 223606.7977\right)}+ \log {223606.7977}=11$ $\log{447213.7977}+ \log{223606.7977}=11$ $5.65+5.35=11$ $11=11$
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