# Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises - Page 395: 15

$\dfrac{1}{2}$

#### Work Step by Step

RECALL: (1) $\log_b{M}+\log_b{N}=\log_b{MN}$ (2) $\log_b{M}−\log_b{N}=\log_b{\frac{M}{N}}$ (3) $\log_b{(b^x)}=x$ (4) $\log_b{b}=1$ Note that $\sqrt{5}=5^{\frac{1}{2}}$. Thus, the given expression is equivalent to: $=\log_5{(5^{\frac{1}{2}})}$ Use rule (3) above to obtain: $=\frac{1}{2}$

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