Given the logarithm equation:
log (2a-3) -2 = log (a+3)
We need to solve for "a"
First we will combine similar terms.
==> log (2a-3) - log (a+3) = 2
Now we will use the logarithm properties to solve.
We know that log a - log b = log a/b
==> log (2a-3)/(a+3) = 2
Now we will rewrite into the exponent form.
==> (2a-3)/(a+3) = 10^2
==> (2a-3)/(a+3) = 100
Now we will multiply by (a+3)
==> 2a -3 = 100(a+3)
==> 2a -3 = 100a +300
==> 98a = -303
==> a = -303/98 = -3.01
But the values of a is not defined for log (2a-3) and log 9a+3)
Then, the equation has no solution.