Solve for x natural log of (2x+4)/5=3

$\ln (\frac{2 x + 4}{5}) = 3$

Step 1

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

$e^{\ln (\frac{2 x + 4}{5})} = e^{3}$

Step 2

Rewrite $\ln (\frac{2 x + 4}{5}) = 3$ 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 $b^{y} = x$ .

$e^{3} = \frac{2 x + 4}{5}$

Step 3

Solve for $x$ .

Rewrite the equation as $\frac{2 x + 4}{5} = e^{3}$ .

$\frac{2 x + 4}{5} = e^{3}$

Multiply both sides by $5$ .

$\frac{2 x + 4}{5} \cdot 5 = e^{3} \cdot 5$

Simplify.

Simplify the left side.

Simplify $\frac{2 x + 4}{5} \cdot 5$ .

Factor $2$ out of $2 x + 4$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 4}{5} \cdot 5 = e^{3} \cdot 5$

Factor $2$ out of $4$ .

$\frac{2 x + 2 \cdot 2}{5} \cdot 5 = e^{3} \cdot 5$

Factor $2$ out of $2 x + 2 \cdot 2$ .

$\frac{2 (x + 2)}{5} \cdot 5 = e^{3} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (x + 2)}{5} \cdot 5 = e^{3} \cdot 5$

Rewrite the expression.

$2 (x + 2) = e^{3} \cdot 5$

Apply the distributive property.

$2 x + 2 \cdot 2 = e^{3} \cdot 5$

Multiply $2$ by $2$ .

$2 x + 4 = e^{3} \cdot 5$

Simplify the right side.

Move $5$ to the left of $e^{3}$ .

$2 x + 4 = 5 e^{3}$

Solve for $x$ .

Subtract $4$ from both sides of the equation.

$2 x = 5 e^{3} - 4$

Divide each term in $2 x = 5 e^{3} - 4$ by $2$ and simplify.

Divide each term in $2 x = 5 e^{3} - 4$ by $2$ .

$\frac{2 x}{2} = \frac{5 e^{3}}{2} + \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5 e^{3}}{2} + \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{5 e^{3}}{2} + \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = \frac{5 e^{3}}{2} - 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 e^{3}}{2} - 2$

Decimal Form:

$x = 48.21384230 \dots$

Solve for x natural log of (2x+4)/5=3

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