Precalculus Examples

$\log_{5} (\sqrt{225}) - \log_{5} (\sqrt{9})$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{5} (\frac{\sqrt{225}}{\sqrt{9}})$

Step 2

Combine $\sqrt{225}$ and $\sqrt{9}$ into a single radical.

$\log_{5} (\sqrt{\frac{225}{9}})$

Step 3

Simplify the expression.

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Step 3.1

Divide $225$ by $9$ .

$\log_{5} (\sqrt{25})$

Step 3.2

Rewrite $25$ as $5^{2}$ .

$\log_{5} (\sqrt{5^{2}})$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\log_{5} (5)$

Step 5

Logarithm base $5$ of $5$ is $1$ .

$1$