Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises: 64

Answer

$-5;7$

Work Step by Step

$\ln \left( 3-x\right) +\ln \left( 5-x\right) =\ln \left( 50-6x\right) \Rightarrow \ln \left[ \left( 3-x\right) \left( 5-x\right) \right] =\ln \left( 50-60x\right) $ $\Rightarrow 15+x^{2}-8x=50-6x\Rightarrow x^{2}-2x-35=0$ $\Rightarrow x_{1},2=\dfrac {-b\pm \sqrt {b^{2}-4ac}}{2a}=\dfrac {2\pm \sqrt {2^{2}-4\times 1\times \left( -35\right) }}{2}=\dfrac {2\pm 12}{2}=-5;7$
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