Solve for x natural log of 4x+1 = natural log of 2x+5

$\ln (4 x + 1) = \ln (2 x + 5)$

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$4 x + 1 = 2 x + 5$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$4 x + 1 - 2 x = 5$

Subtract $2 x$ from $4 x$ .

$2 x + 1 = 5$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$2 x = 5 - 1$

Subtract $1$ from $5$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$