Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.7 - Common Logarithms, Natural Logarithms, and Change of Base - Exercise Set: 44

Answer

$x=e^{-3.7}\approx.0247$

Work Step by Step

We are given the equation $\ln(x)=-3.7$. To solve for x, remember that the base of a natural logarithm is understood to be $e$. Therefore, $\ln(x)=log_{e}x=-3.7$. If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$. Therefore, $x=e^{-3.7}\approx.0247$.
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