- #1

opus

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## Homework Statement

Solve:

##ln(x-4)-ln(x)=6##

I know the solution is

**no solution,**but the value I got is what I am unsure of as I could have got a million different values for x that would result in no solution, but I'm not sure if the value that I got is correct. Once you hit the "no solution" button for the homework, it tells you if you're right or wrong and doesn't tell you the correct value of x.

## Homework Equations

## The Attempt at a Solution

(i) $$ln\left(\frac{x-4}{x}\right)=6$$

(ii) $$e^{ln\left(\frac{x-4}{x}\right)}=e^6$$

(iii) $$\frac{x-4}{x}=6$$

(iv) $$x-4=6x$$

(v) $$-4=5x$$

(vi) $$x=\frac{-4}{5}$$

(v) x=negative so there is

**no solution**

Step (iii) is where I'm questioning myself. I know that step (iv) results from (iii), but I can't seem to justify (iii) and how I just made the expressions exponents of the base e.