Question 201509
this can only be true if 4x = x-5.

solve for x and you have the answer.

subtract x from both sides of the equation to get

4x - x = -5

simplify to get

3x = -5

divide both sides of the equation to get

x =  -5/3

that's your answer.

substitute in the equation to get

ln (4*(-5/3) = ln (-5/3 - 5)

simplify to get

ln (-20/3) = ln (-5/3 - 15/3)

simplify further to get

ln (-20/3) = ln (-20/3)

since this is an identity, it proves your answer is correct.

the problem I see here is that you are trying to take the natural log of a negative number.

all logs have to greater than 0.

negative numbers or 0 are not allowed.

if I have done this correctly, then the value of x is correct and the natural log cannot be found.

I used the calculator to try to get the answer but the calculator said the logarithm can't be found.

to prove the logic is correct, I'll give you one that can be found.

take ln (4x) = ln (x + 15)

this can only be true if 4x = x + 15

this is true if x = 5 because 4 * 5 = 5 + 15.

your answer would be x = 5 and you would have ln (20) = ln (20) which is an identify again only this time it can be solved.