Solve for x 4 natural log of 6x=20

$4 \ln (6 x) = 20$

Step 1

Divide each term in $4 \ln (6 x) = 20$ by $4$ and simplify.

Divide each term in $4 \ln (6 x) = 20$ by $4$ .

$\frac{4 \ln (6 x)}{4} = \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \ln (6 x)}{4} = \frac{20}{4}$

Divide $\ln (6 x)$ by $1$ .

$\ln (6 x) = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$\ln (6 x) = 5$

Step 2

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

$e^{\ln (6 x)} = e^{5}$

Step 3

Rewrite $\ln (6 x) = 5$ 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 $b^{y} = x$ .

$e^{5} = 6 x$

Step 4

Solve for $x$ .

Rewrite the equation as $6 x = e^{5}$ .

$6 x = e^{5}$

Divide each term in $6 x = e^{5}$ by $6$ and simplify.

Divide each term in $6 x = e^{5}$ by $6$ .

$\frac{6 x}{6} = \frac{e^{5}}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{e^{5}}{6}$

Divide $x$ by $1$ .

$x = \frac{e^{5}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{5}}{6}$

Decimal Form:

$x = 24.73552651 \dots$

Solve for x 4 natural log of 6x=20

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