Solve for x natural log of 2x+3=7

$\ln (2 x + 3) = 7$

Step 1

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

$e^{\ln (2 x + 3)} = e^{7}$

Step 2

Rewrite $\ln (2 x + 3) = 7$ 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 $b^{y} = x$ .

$e^{7} = 2 x + 3$

Step 3

Solve for $x$ .

Rewrite the equation as $2 x + 3 = e^{7}$ .

$2 x + 3 = e^{7}$

Subtract $3$ from both sides of the equation.

$2 x = e^{7} - 3$

Divide each term in $2 x = e^{7} - 3$ by $2$ and simplify.

Divide each term in $2 x = e^{7} - 3$ by $2$ .

$\frac{2 x}{2} = \frac{e^{7}}{2} + \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{e^{7}}{2} + \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{e^{7}}{2} + \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{e^{7}}{2} - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{7}}{2} - \frac{3}{2}$

Decimal Form:

$x = 546.81657921 \dots$

Solve for x natural log of 2x+3=7

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