Solve for x natural log of 5x=4

$\ln (5 x) = 4$

Step 1

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

$e^{\ln (5 x)} = e^{4}$

Step 2

Rewrite $\ln (5 x) = 4$ 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 $b^{y} = x$ .

$e^{4} = 5 x$

Step 3

Solve for $x$ .

Rewrite the equation as $5 x = e^{4}$ .

$5 x = e^{4}$

Divide each term in $5 x = e^{4}$ by $5$ and simplify.

Divide each term in $5 x = e^{4}$ by $5$ .

$\frac{5 x}{5} = \frac{e^{4}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{e^{4}}{5}$

Divide $x$ by $1$ .

$x = \frac{e^{4}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{4}}{5}$

Decimal Form:

$x = 10.91963000 \dots$

Solve for x natural log of 5x=4

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