Precalculus Examples

$\log (\frac{1}{3}) \cdot 243$

Step 1

Multiply $\log (\frac{1}{3}) \cdot 243$ .

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Step 1.1

Reorder $\log (\frac{1}{3})$ and $243$ .

$243 \cdot \log (\frac{1}{3})$

Step 1.2

Simplify $243 \cdot \log (\frac{1}{3})$ by moving $243$ inside the logarithm.

$\log ({(\frac{1}{3})}^{243})$

Step 2

Apply the product rule to $\frac{1}{3}$ .

$\log (\frac{1^{243}}{3^{243}})$

Step 3

One to any power is one.

$\log (\frac{1}{3^{243}})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{1}{3^{243}})$

Decimal Form:

$- 115.94046489 \dots$