Algebra Examples

$\ln (x) = - 4$

Step 1

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

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

Step 2

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

$e^{- 4} = x$

Step 3

Solve for $x$ .

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Step 3.1

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

$x = e^{- 4}$

Step 3.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{e^{4}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{e^{4}}$

Decimal Form:

$x = 0.01831563 \dots$