Solve for x 4 natural log of x=-2

$4 \ln (x) = - 2$

Divide each term in $4 \ln (x) = - 2$ by $4$ and simplify.

Divide each term in $4 \ln (x) = - 2$ by $4$ .

$\frac{4 \ln (x)}{4} = \frac{- 2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \ln (x)}{4} = \frac{- 2}{4}$

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

$\ln (x) = \frac{- 2}{4}$

Simplify the right side.

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

$\ln (x) = \frac{2 (- 1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\ln (x) = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$\ln (x) = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$\ln (x) = \frac{- 1}{2}$

Move the negative in front of the fraction.

$\ln (x) = - \frac{1}{2}$

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

$e^{\ln (x)} = e^{- \frac{1}{2}}$

Rewrite $\ln (x) = - \frac{1}{2}$ 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 $b^{y} = x$ .

$e^{- \frac{1}{2}} = x$

Solve for $x$ .

Rewrite the equation as $x = e^{- \frac{1}{2}}$ .

$x = e^{- \frac{1}{2}}$

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

$x = \frac{1}{e^{\frac{1}{2}}}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{e^{\frac{1}{2}}}$

Decimal Form:

$x = 0.60653065 \dots$

Solve for x 4 natural log of x=-2

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