Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Review - Exercises: 66

Answer

This equation has no solutions

Work Step by Step

$\ln(x-2)+\ln3=\ln(5x-7)$ Combine the sum on the left side of the equation as the logarithm of a product: $\ln3(x-2)=\ln(5x-7)$ Evaluate the product inside the $\ln$ on the left side: $\ln(3x-6)=\ln(5x-7)$ If $\ln(3x-6)=\ln(5x-7)$, then $3x-6=5x-7$ $3x-6=5x-7$ Solve for $x$: $3x-5x=-7+6$ $-2x=-1$ $x=\dfrac{1}{2}$ Check the solution found by plugging them into the original equation: $\ln\Big(\dfrac{1}{2}-2\Big)+\ln3=\ln\Big[5\Big(\dfrac{1}{2}\Big)-7\Big]$ False This equation has no solutions
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