Solve for x -7+ natural log of 2x=4

$- 7 + \ln (2 x) = 4$

Step 1

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

Add $7$ to both sides of the equation.

$\ln (2 x) = 4 + 7$

Add $4$ and $7$ .

$\ln (2 x) = 11$

Step 2

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

$e^{\ln (2 x)} = e^{11}$

Step 3

Rewrite $\ln (2 x) = 11$ 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 $b^{y} = x$ .

$e^{11} = 2 x$

Step 4

Solve for $x$ .

Rewrite the equation as $2 x = e^{11}$ .

$2 x = e^{11}$

Divide each term in $2 x = e^{11}$ by $2$ and simplify.

Divide each term in $2 x = e^{11}$ by $2$ .

$\frac{2 x}{2} = \frac{e^{11}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{e^{11}}{2}$

Divide $x$ by $1$ .

$x = \frac{e^{11}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{11}}{2}$

Decimal Form:

$x = 29937.07085759 \dots$

Solve for x -7+ natural log of 2x=4

Related Questions

Support LCMGCF.com by disabling your adblocker.