QuestionFind the value of $\log _{5} \sqrt{5}$ . Options: a) 2 b) -2 c) $\frac{1}{2}$ d) $\frac{-1}{2}$ e) 0

Studdy Solution

STEP 1

Assumptions1. The base of the logarithm is5. . The argument of the logarithm is $\sqrt{5}$ .
3. We need to find the value of $\log{5} \sqrt{5}$ .

STEP 2

We know that $\sqrt{5}$ can be written as $5^{\frac{1}{2}}$ . So, we replace $\sqrt{5}$ with $5^{\frac{1}{2}}$ in the logarithm.
$\log{5} \sqrt{5} = \log{5}5^{\frac{1}{2}}$

STEP 3

We use the property of logarithms that $\log{b} b^{x} = x$ . This property states that the logarithm base $b$ of $b$ raised to the power of $x$ is equal to $x$ .
So, we apply this property to our expression.
$\log{5}5^{\frac{1}{2}} = \frac{1}{2}$ So, $\log{5} \sqrt{5} = \frac{1}{2}$ .
The solution is c) $\frac{1}{2}$ .

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