Solve for x natural log of 2x-3=3/2

$\ln (2 x - 3) = \frac{3}{2}$

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

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

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

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

Solve for $x$ .

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

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

Add $3$ to both sides of the equation.

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 3.74084453 \dots$

Solve for x natural log of 2x-3=3/2

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