Solve for x 3+4 natural log of 2x=15

$3 + 4 \ln (2 x) = 15$

Move all terms not containing $\ln (2 x)$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$4 \ln (2 x) = 15 - 3$

Subtract $3$ from $15$ .

$4 \ln (2 x) = 12$

Divide each term in $4 \ln (2 x) = 12$ by $4$ and simplify.

Divide each term in $4 \ln (2 x) = 12$ by $4$ .

$\frac{4 \ln (2 x)}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \ln (2 x)}{4} = \frac{12}{4}$

Divide $\ln (2 x)$ by $1$ .

$\ln (2 x) = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$\ln (2 x) = 3$

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

$e^{\ln (2 x)} = e^{3}$

Rewrite $\ln (2 x) = 3$ 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 $b^{y} = x$ .

$e^{3} = 2 x$

Solve for $x$ .

Rewrite the equation as $2 x = e^{3}$ .

$2 x = e^{3}$

Divide each term in $2 x = e^{3}$ by $2$ and simplify.

Divide each term in $2 x = e^{3}$ by $2$ .

$\frac{2 x}{2} = \frac{e^{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{e^{3}}{2}$

Divide $x$ by $1$ .

$x = \frac{e^{3}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{3}}{2}$

Decimal Form:

$x = 10.04276846 \dots$

Solve for x 3+4 natural log of 2x=15

Related Questions

Support LCMGCF.com by disabling your adblocker.