Precalculus Examples

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

Step 1

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

$9 \log (27 \sqrt{y})$

Step 2

Simplify $9 \log (27 \sqrt{y})$ by moving $9$ inside the logarithm.

$\log ({(27 \sqrt{y})}^{9})$

Step 3

Apply the product rule to $27 \sqrt{y}$ .

$\log (27^{9} {\sqrt{y}}^{9})$

Step 4

Raise $27$ to the power of $9$ .

$\log (7625597484987 {\sqrt{y}}^{9})$

Step 5

Rewrite ${\sqrt{y}}^{9}$ as $\sqrt{y^{9}}$ .

$\log (7625597484987 \sqrt{y^{9}})$

Step 6

Rewrite $y^{9}$ as ${(y^{4})}^{2} y$ .

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Step 6.1

Factor out $y^{8}$ .

$\log (7625597484987 \sqrt{y^{8} y})$

Step 6.2

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\log (7625597484987 \sqrt{{(y^{4})}^{2} y})$

Step 7

Pull terms out from under the radical.

$\log (7625597484987 y^{4} \sqrt{y})$