Precalculus Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

$\log (8) + \log (\frac{9}{3})$

Step 2.3

Divide $9$ by $3$ .

$\log (8) + \log (3)$

Step 3

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

$\log (8 \cdot 3)$

Step 4

Multiply $8$ by $3$ .

$\log (24)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (24)$

Decimal Form:

$1.38021124 \dots$