Precalculus Examples

$\log (3) \sqrt{27}$

Step 1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1

Factor $9$ out of $27$ .

$\log (3) \sqrt{9 (3)}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\log (3) \sqrt{3^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$\log (3) (3 \sqrt{3})$

Step 3

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

$\log (3^{3}) \sqrt{3}$

Step 4

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

$\log (27) \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (27) \sqrt{3}$

Decimal Form:

$2.47919476 \dots$