Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 31

Answer

$x=\dfrac{\log\dfrac{50}{3}}{\log4}\approx2.029447$

Work Step by Step

$4^{x}+2^{1+2x}=50$ We can rewrite the expression on the left side of the equation using the product of powers of the same base rule: $4^{x}+(2)(2^{2x})=50$ Apply the power of a power rule to the second term of the left side of the equation: $4^{x}+(2)(2^{2})^{x}=50$ $4^{x}+(2)(4^{x})=50$ Simplify and solve for $4^{x}$: $3(4^{x})=50$ $4^{x}=\dfrac{50}{3}$ Apply $\log$ to both sides of the equation: $\log4^{x}=\log\dfrac{50}{3}$ The exponent $x$ can be taken down to multiply in front of the $\ln$: $x\log4=\log\dfrac{50}{3}$ Solve for $x$: $x=\dfrac{\log\dfrac{50}{3}}{\log4}\approx2.029447$
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