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Solving Log Equations

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