Precalculus Examples

$\log_{3} (7 x) = 2$

Step 1

Rewrite $\log_{3} (7 x) = 2$ 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 $b^{y} = x$ .

$3^{2} = 7 x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $7 x = 3^{2}$ .

$7 x = 3^{2}$

Step 2.2

Divide each term in $7 x = 3^{2}$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 x = 3^{2}$ by $7$ .

$\frac{7 x}{7} = \frac{3^{2}}{7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{3^{2}}{7}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3^{2}}{7}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raise $3$ to the power of $2$ .

$x = \frac{9}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{7}$

Decimal Form:

$x = 1.\overline{285714}$

Mixed Number Form:

$x = 1 \frac{2}{7}$