Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

Raise $3$ to the power of $5$ .

$2 \log (243) + \log ({(3)}^{2})$

Step 1.2

Simplify $2 \log (243)$ by moving $2$ inside the logarithm.

$\log (243^{2}) + \log ({(3)}^{2})$

Step 1.3

Raise $243$ to the power of $2$ .

$\log (59049) + \log ({(3)}^{2})$

Step 1.4

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

$\log (59049) + \log (9)$

Step 2

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

$\log (59049 \cdot 9)$

Step 3

Multiply $59049$ by $9$ .

$\log (531441)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (531441)$

Decimal Form:

$5.72545505 \dots$