Calculus Examples

$9 \ln (x) = 1$

Step 1

Divide each term in $9 \ln (x) = 1$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 \ln (x) = 1$ by $9$ .

$\frac{9 \ln (x)}{9} = \frac{1}{9}$

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.

$\frac{9 \ln (x)}{9} = \frac{1}{9}$

Step 1.2.1.2

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

$\ln (x) = \frac{1}{9}$

Step 2

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

$e^{\ln (x)} = e^{\frac{1}{9}}$

Step 3

Rewrite $\ln (x) = \frac{1}{9}$ 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 $b^{y} = x$ .

$e^{\frac{1}{9}} = x$

Step 4

Rewrite the equation as $x = e^{\frac{1}{9}}$ .

$x = e^{\frac{1}{9}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = e^{\frac{1}{9}}$

Decimal Form:

$x = 1.11751906 \dots$