Precalculus Examples

$(\frac{1}{2}) \log (3) (\frac{1}{81})$

Step 1

Simplify $(\frac{1}{2}) \log (3)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (3^{\frac{1}{2}}) \frac{1}{81}$

Step 2

Multiply $\log (3^{\frac{1}{2}}) \frac{1}{81}$ .

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Step 2.1

Reorder $\log (3^{\frac{1}{2}})$ and $\frac{1}{81}$ .

$\frac{1}{81} \log (3^{\frac{1}{2}})$

Step 2.2

Simplify $\frac{1}{81} \log (3^{\frac{1}{2}})$ by moving $\frac{1}{81}$ inside the logarithm.

$\log ({(3^{\frac{1}{2}})}^{\frac{1}{81}})$

Step 3

Multiply the exponents in ${(3^{\frac{1}{2}})}^{\frac{1}{81}}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (3^{\frac{1}{2} \cdot \frac{1}{81}})$

Step 3.2

Multiply $\frac{1}{2} \cdot \frac{1}{81}$ .

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Step 3.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{81}$ .

$\log (3^{\frac{1}{2 \cdot 81}})$

Step 3.2.2

Multiply $2$ by $81$ .

$\log (3^{\frac{1}{162}})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (3^{\frac{1}{162}})$

Decimal Form:

$0.00294519 \dots$