Precalculus Examples

$2 \log (3) + \log (5) - \log (9)$

Step 1

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

$2 \log (3) + \log (\frac{5}{9})$

Step 2

Simplify each term.

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Step 2.1

Simplify $2 \log (3)$ by moving $2$ inside the logarithm.

$\log (3^{2}) + \log (\frac{5}{9})$

Step 2.2

Raise $3$ to the power of $2$ .

$\log (9) + \log (\frac{5}{9})$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (9 (\frac{5}{9}))$

Step 4

Cancel the common factor of $9$ .

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Step 4.1

Cancel the common factor.

$\log (9 (\frac{5}{9}))$

Step 4.2

Rewrite the expression.

$\log (5)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (5)$

Decimal Form:

$0.69897000 \dots$