Precalculus Examples

$\log_{3} (5 x) = 4$

Step 1

Rewrite $\log_{3} (5 x) = 4$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$3^{4} = 5 x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $5 x = 3^{4}$ .

$5 x = 3^{4}$

Step 2.2

Divide each term in $5 x = 3^{4}$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 x = 3^{4}$ by $5$ .

$\frac{5 x}{5} = \frac{3^{4}}{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{3^{4}}{5}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3^{4}}{5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raise $3$ to the power of $4$ .

$x = \frac{81}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{81}{5}$

Decimal Form:

$x = 16.2$

Mixed Number Form:

$x = 16 \frac{1}{5}$