Algebra Examples

$\ln (x) = 6$

Step 1

To solve for

$x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x)} = e^{6}$

Step 2

Rewrite

$\ln (x) = 6$ 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

$b^{y} = x$ .

$e^{6} = x$

Step 3

Rewrite the equation as

$x = e^{6}$ .

$x = e^{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = e^{6}$

Decimal Form:

$x = 403.42879349 \dots$