Question

Let me know if I got this right

What is the solution to the equation?

lnx−ln(4x−1)=ln5

Enter your answer in the box. Enter any fractions as simplified fractions.

Answer 1

x = 5/19

Explanation:

For left side, apply logarithm division property:

`\displaystyle{ \ln a - \ln b= \ln \left( (a)/(b) \right)}`

Hence:

`\displaystyle{ \ln \left( (x)/(4x - 1) \right) = \ln 5}`

Since both sides have same ln, we can cancel ln both sides:

`\displaystyle{ (x)/(4x - 1) = 5}`

Solve the equation for x:

`\displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = (5)/(19)}`

Therefore, x = 5/19