Solve the logarithm equation:log (2x-2) = log (x-2) + 1

log (2x-2) = log (x-2) + 1

we will
use logarithm properties to find the value of x.

First we know that
log 10 = 1

==> log (2x-2) = log (x-2) + log
10

Now we know that log a + log b = log
ab

==> log (2x-2) = log
(10*(x-2)

==> log (2x-2) = log (10x
-20)

Now, we know that if log a = log b ==> a =
b

==> (2x-2) = 10x
-20

==> 8x = 18

==> x =
18/8= 9/4= 2.25

Then the solution to the equation is
9/4 = 2.25.