Please can someone solve this and show me step by step how they did it?

Question

Solve the equation.

ln 6 + ln (x - 1) = 0

Answer 1

One rule for logarithms (of any base) is that the sum of logs = the log of the product, so

ln 6 + ln (x - 1) = 0
becomes
ln (6*(x - 1)) = 0

Then change it to exponential form (distribute as you go):
e^0 = 6x - 6
anything to the 0 power = 1, so
1 = 6x - 6
7 = 6x
x = 7/6

Answer 2

Subtract ln(6) from both sides:
ln( x - 1 ) = - ln(6)

Remember the rule k ln(x) = ln(x^k)
ln( x - 1 ) = ln (6^-1)
ln( x - 1 ) = ln (1/6)

You now have two natural logs that are equal:
x - 1 = 1/6

Add 1 to both sides:
x = 7/6

Answer 3

If I remember right:

6 + ln (x-1) = 0
ln ( x - 1) = -6
x-1 = -60
x = -59