Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set: 24

Answer

$\frac{1}{2}\log_5{x}-2$

Work Step by Step

RECALL: (1) $\log_b{(MN)} = \log_b{M} + \log_b{N}$ (2) $\log_b{(\frac{M}{N})} = \log_b{M} - \log_b{N}$ (3) $\log_b{(b^x)}=x$ (4) $\log_b{(a^n)} = n \cdot \log_b{a}$ (5) $\sqrt{x} = x^{\frac{1}{2}}$ Use rule (2) above to obtain $=\log_5{(\sqrt{x})}-\log_5{25} \\=\log_5{(\sqrt{x})}-\log_5{(5^2)}$ Use rule (5) above to obtain: $=\log_5{(x^{\frac{1}{2}})}-\log_5{(5^2)}$ Use rule (4) above to obtain: $=\frac{1}{2}\log_5{x}-\log_5{(5^2)}$ Use rule (3) above to obtain: $=\frac{1}{2}\log_5{x}-2$
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