Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Lesson Check - Page 473: 6


Yes, it is possible. Example: $2^x=0$

Work Step by Step

We are asked if it is possible for an exponential equation to have no solution. This is indeed possible. Consider: $2^x=0$ We know that this equation has no solution because the graph of $y=2^x$ is always above the $x-axis$. The $y$ values get asymptotically close to zero, but never reach the value of $0$. Similarly, $2^x=-1$ would also have no solution, since $2^x$ is never negative.
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