Question

Find all solutions to the equation 4ln(5x)+5=2. Show your work.

Answer 1

Given the equation:

`4\ln \mleft(5x\mright)+5=2`

We will find the value of (x) as follows:

a) subtract 5 from both sides

`\begin{gathered} 4\ln \mleft(5x\mright)+5-5=2-5 \\ 4\ln \mleft(5x\mright)=-3 \end{gathered}`

b) Divide both sides by 4

`\ln (5x)=-(3)/(4)`

c) Taking the exponential of both sides to remove ln

`5x=e^{-(3)/(4)}`

Finally, divide both sides by 5

`x=(1)/(5)e^{-(3)/(4)}\approx0.09447`

So, the answer will be x = 0.09447