# How do you solve ln(4x+1)-ln3=5?

Nov 11, 2016

Please see the explanation for steps leading to: $x = \frac{3 {e}^{5} - 1}{4}$

#### Explanation:

Use the property of logarithms ${\log}_{b} \left(x\right) - {\log}_{b} \left(y\right) = {\log}_{b} \left(\frac{x}{y}\right)$:

$\ln \left(\frac{4 x + 1}{3}\right) = 5$

Write both sides as exponents of e:

${e}^{\ln \left(\frac{4 x + 1}{3}\right)} = {e}^{5}$

Use the property ${e}^{\ln} \left(a\right) = a$:

$\frac{4 x + 1}{3} = {e}^{5}$

Multiply both side by 3:

$4 x + 1 = 3 {e}^{5}$

Subtract 1 from both sides:

$4 x = 3 {e}^{5} - 1$

Divide both sides by 4:

$x = \frac{3 {e}^{5} - 1}{4}$