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Most simply put, logarithms are inverses of exponentials.

Check it out:

Let's graph the inverse of

y = 2^( x )

Remember that every ( x , y ) has a ( y , x ) partner, so we'll graph this guy...  then nail his inverse!

graph of y = 2^( x ) ... includes the points ( -1 , 1 / 2 ) , ( 0 , 1 ) , ( 1 , 2 ) and ( 2 , 4 )

graph of the inverse of y = 2^( x ) ... includes the points ( 1 / 2 , -1 ) , ( 1 , 0 ) , ( 2 , 1 ) and ( 4 , 2 )

This is the inverse of

y = 2^( x )

Remember the steps to find the inverse of a function using algebra?  In one part, you switch the x and the y -- right?

So, we COULD say that the inverse of

y = 2^( x )isx = 2^( y )...

But...  ya know...  in math, we really like to write things like

y = x stuff