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: 12

Answer

(a) $x = -2\cdot \log{2}$ (b) $x\approx -0.602060$

Work Step by Step

(a) Take the common logarithm of both sides to obtain: $\log{10^{-x}} = \log{4}$ Use the rule $\log{10^n} = n$ to obtain: $-x = \log{4} \\-x=\log{(2^2)} \\-1(-x) = -1(\log{(2^2)} \\x = -\log{(2^2)}$ Use the rule $\log{(a^n)} = n\log{a}$ to obtain: $x = -2\cdot \log{2}$ (b) Use a calculator to evaluate the answer and have: $x =-2(0.3010299957) \\x\approx -0.602060$
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