Question

How do you solve this multi-step equation involving natural logarithms?

ln(x-3)-ln5=1

Answer 1

Explanation:

Step 1, when subtracting logs with the same base you can rewrite it with one log and the argument becomes division...

ln(x - 3) - ln 5 = 1 becomes...

ln [ (x - 3)/5 ] = 1

Step 2, rewrite the by putting into exponential form...ln has a base of e, so we get..

e^1 = (x -3)/5

Now solve...

e = (x - 3)/5

5e = x - 3

5e + 3 = x