Precalculus Examples

$9 \log_{3} (0.1 x) = 17$

Step 1

Divide each term in $9 \log_{3} (0.1 x) = 17$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 \log_{3} (0.1 x) = 17$ by $9$ .

$\frac{9 \log_{3} (0.1 x)}{9} = \frac{17}{9}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9 \log_{3} (0.1 x)}{9} = \frac{17}{9}$

Step 1.2.1.2

Divide $\log_{3} (0.1 x)$ by $1$ .

$\log_{3} (0.1 x) = \frac{17}{9}$

Step 2

Rewrite $\log_{3} (0.1 x) = \frac{17}{9}$ 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 $b^{y} = x$ .

$3^{\frac{17}{9}} = 0.1 x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $0.1 x = 3^{\frac{17}{9}}$ .

$0.1 x = 3^{\frac{17}{9}}$

Step 3.2

Divide each term in $0.1 x = 3^{\frac{17}{9}}$ by $0.1$ and simplify.

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Step 3.2.1

Divide each term in $0.1 x = 3^{\frac{17}{9}}$ by $0.1$ .

$\frac{0.1 x}{0.1} = \frac{3^{\frac{17}{9}}}{0.1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.1$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.1 x}{0.1} = \frac{3^{\frac{17}{9}}}{0.1}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3^{\frac{17}{9}}}{0.1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $17$ by $9$ .

$x = \frac{3^{1.\overline{8}}}{0.1}$

Step 3.2.3.2

Raise $3$ to the power of $1.\overline{8}$ .

$x = \frac{7.96579336}{0.1}$

Step 3.2.3.3

Divide $7.96579336$ by $0.1$ .

$x = 79.65793368$