Now for some form #2 critters:

SolveLog to the base 5( x - 6 ) = Log to the base 5( 7 )

Both sides are logs...  But, that's no problem since they are the same base (5).

Hit it with the inverse!

5^( Log to the base 5( x - 6 ) ) = 5^( Log to the base 5( 7 ) )  ...  the 5 and the Log to the base 5 on both sides cancel  ...  x - 6 = 7  ...  x = 13

Look back at the original... 
Easy to see that the answer is
13!

Here's another one:

SolveLog( x^( 2 ) - x ) = Log( 6 )

Zap 'em!

10^( Log( x^( 2 ) - x ) = 10^( Log( 6 ) )  ...  the 10 and the Log cancel on both sides  ...  x^( 2 ) - x = 6  ...  one of our old quadratic friends!  ...  x^( 2 ) - x - 6 = 0  ...  ( x - 3 ) ( x + 2 ) = 0  ...  x - 3 = 0  or  x + 2 = 0  ...  x = 3  ...  x = -2