Precalculus Examples

$\log_{5} (125^{x}) = - 3$

Step 1

Expand $\log_{5} (125^{x})$ .

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Step 1.1

Expand $\log_{5} (125^{x})$ by moving $x$ outside the logarithm.

$x \log_{5} (125)$

Step 1.2

Logarithm base $5$ of $125$ is $3$ .

$x \cdot 3$

Step 2

The expanded equation is $x \cdot 3 = - 3$ .

$x \cdot 3 = - 3$

Step 3

Divide each term in $x \cdot 3 = - 3$ by $3$ and simplify.

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Step 3.1

Divide each term in $x \cdot 3 = - 3$ by $3$ .

$\frac{x \cdot 3}{3} = \frac{- 3}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \cdot 3}{3} = \frac{- 3}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 3$ by $3$ .

$x = - 1$