Advertisement

OK, ready to go!  Let's start by doing some that are already in the nice forms:

Log to the base 2( 4x ) = 3
We can't solve anything with this
obnoxious Log in here -- he's blocking
the
x!  So...  We need to get rid
 of him.  And who can do that?
His inverse!

So...  Zap both sides with2^x!

2^( Log to the base 2( 4x ) ) = 2^3  ...  the 2 and the Log to the base 2 cancel out  ...  4x = 8  ...  Now, it's easy!  ...  x = 2

With that inverse trick, these are really pretty simple.

Let's do some more:

Solve Log( 50x ) = 3
Remember that this is really

Log to the base 10( 50x ) = 3

Hit it with the inverse:

10^( Log( 50x ) ) = 10^3  ...  the 10 and the Log cancel out  ...  50x = 1000  ...  x = 20