What if the log equations aren't all set up in form #1 or form #2 to zap with the inverse?

No problem!  We just use the combining trick from a couple of sections ago.

It's really easy!

Remember that there are two forms to aim for:

1 )  Log( blob ) = #
 We'll go for this one when there is a term
in the equation that's just a number without a log.

 

2 )  Log( blob ) = Log( blob )
 We'll go for this one when every term
in the equation has a log.

Check it out:

Solve

Log to the base 2( 3 ) + Log to the base 2( x ) = Log to the base 2( 5 ) + Log to the base 2( x - 2 )

Everyone has a log, so it's form #2.

To get it set up, just combine each side:

Log to the base 2( 3x ) = Log to the base 2( 5( x - 2 ) )

Now, zap it with the inverse:

2^( Log to the base 2( 3x ) ) = 2^( Log to the base 2( 5( x - 2 ) )  ...  the 2 and the Log to the base 2 cancel on both sides  ...  3x = 5( x - 2 )  ...  3x = 5x - 10  ...  -2x = -10  ...  x = 5