Finite Math Examples

$9 \ln (8 x) = 36$

Step 1

Divide each term in $9 \ln (8 x) = 36$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 \ln (8 x) = 36$ by $9$ .

$\frac{9 \ln (8 x)}{9} = \frac{36}{9}$

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.

$\frac{9 \ln (8 x)}{9} = \frac{36}{9}$

Step 1.2.1.2

Divide $\ln (8 x)$ by $1$ .

$\ln (8 x) = \frac{36}{9}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $36$ by $9$ .

$\ln (8 x) = 4$

Step 2

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (8 x)} = e^{4}$

Step 3

Rewrite $\ln (8 x) = 4$ 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 $b^{y} = x$ .

$e^{4} = 8 x$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $8 x = e^{4}$ .

$8 x = e^{4}$

Step 4.2

Divide each term in $8 x = e^{4}$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = e^{4}$ by $8$ .

$\frac{8 x}{8} = \frac{e^{4}}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{e^{4}}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{e^{4}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{4}}{8}$

Decimal Form:

$x = 6.82476875 \dots$