Answer:
x = 5/19
Step-by-step explanation:
For left side, apply logarithm division property:
[tex] \displaystyle{ \ln a - \ln b= \ln \left( \dfrac{a}{b} \right)}[/tex]
Hence:
[tex] \displaystyle{ \ln \left( \dfrac{x}{4x - 1} \right) = \ln 5}[/tex]
Since both sides have same ln, we can cancel ln both sides:
[tex] \displaystyle{ \dfrac{x}{4x - 1} = 5}[/tex]
Solve the equation for x:
[tex] \displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = \dfrac{5}{19}}[/tex]
Therefore, x = 5/19
