SOLUTION: ln(4x)=ln(x-5). Solve, can you please help me?

Question 201509: ln(4x)=ln(x-5). Solve, can you please help me?

Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If two logs to the same base are equal, then their arguments must be equal, that is to say:

And since is the same thing as , given , you can say:

Solve for

But that value of means that . Hence is not in the domain of . Therefore there is no solution.

John

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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