College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises: 6

Answer

The solution is $x=\left\{1\right\}$.

Work Step by Step

Since $\dfrac{1}{10}=10^{-1}$, then the given equation is equivalent to: $10^{2x-3}=10^{-1}$ Use the property $a^m = a^n \longrightarrow m=n$ to obtain: $\begin{array}{ccc} &2x-3&=&-1 \\&2x-3+3&=&-1+3 \\&2x&=&2 \\&\dfrac{2x}{2} &= &\dfrac{2}{2} \\&x&=&1 \end{array}$ Thus, the solution is $x=\left\{1\right\}$.
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