Algebra Examples

$2 \ln (x) = 6$

Step 1

Divide each term in $2 \ln (x) = 6$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \ln (x) = 6$ by $2$ .

$\frac{2 \ln (x)}{2} = \frac{6}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \ln (x)}{2} = \frac{6}{2}$

Step 1.2.1.2

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

$\ln (x) = \frac{6}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $6$ by $2$ .

$\ln (x) = 3$

Step 2

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

$e^{\ln (x)} = e^{3}$

Step 3

Rewrite $\ln (x) = 3$ 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 $b^{y} = x$ .

$e^{3} = x$

Step 4

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

$x = e^{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = e^{3}$

Decimal Form:

$x = 20.08553692 \dots$