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: 58

Answer

$log_{6}8\approx1.1606$

Work Step by Step

In order to evaluate the given logarithm, we can use the change of base formula. $log_{b}a=\frac{log_{c}a}{log_{c}b}$ (where a, b, and c are positive real numbers and neither b nor c is 1) For simplicity, we will use base 10, which is the base of the common logarithm. Therefore, $log_{6}8=\frac{log_{10}8}{log_{10}6}=\frac{.9031}{.7782}\approx1.1606$.
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