Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1 - Page 419: 14

Answer

$$\log \left( {\frac{{100{x^{1/2}}}}{{{{\sin }^3}2x}}} \right)$$

Work Step by Step

$$\eqalign{ & \frac{1}{2}\log x - 3\log \left( {\sin 2x} \right) + 2 \cr & {\text{use the power property for logarithms }}\log {a^n} = n\log a \cr & = \log {x^{1/2}} - \log {\left( {\sin 2x} \right)^3} + \log 100 \cr & {\text{use the quotient property for logarithms}} \cr & = \log \left( {\frac{{{x^{1/2}}}}{{{{\sin }^3}2x}}} \right) + \log 100 \cr & {\text{use the product property for logarithms}} \cr & = \log \left( {\frac{{100{x^{1/2}}}}{{{{\sin }^3}2x}}} \right) \cr} $$
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