Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Review - Exercises: 64



Work Step by Step

$3^{2x}-3^{x}-6=0$ Let $3^{x}$ be equal to $u$: $u=3^{x}$ $u^{2}=3^{2x}$ Rewrite the original equation using the new variable $u$: $u^{2}-u-6=0$ Solve this equation by factoring: $(u-3)(u+2)=0$ Set both factors equal to $0$ and solve each individual equation for $u$: $u-3=0$ $u=3$ $u+2=0$ $u=-2$ Substitute $u$ back to $3^{x}$ and solve for $x$: $3^{x}=3$ If $3^{x}=3$, then $x=1$ $x=1$ $3^{x}=-2$ There are no values of $x$ that make this equation true. The solution found is $x=1$
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