# How do you solve ln(4x+1)=ln(2x+5)?

Jul 11, 2016

$x = 2$

#### Explanation:

Remembering that taking the exponential of a natural logarithm gets rid of the natural logarithm, we can apply it in this case to have a simpler equation, giving us

${\cancel{e}}^{\cancel{\ln} \left(4 x + 1\right)} = {\cancel{e}}^{\cancel{\ln} \left(2 x + 5\right)}$

$4 x + 1 = 2 x + 5$

Now, subtracting $2 x$ from both sides yields

$2 x + 1 = 5$

Subtracting $1$ from both sides gives us

$2 x = 4$, so $x = 2$