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So, instead of writing

x = 2^( y )

we give it a special inverse name:

y = log to the base 2( x )

So, the inverse of y = 2^( x )isy = log to the base 2( x )!

Remember that the base of our exponential guy is 2:

y = 2^( x ) ... the 2 is the base

So, the base of the corresponding logarithm is 2:

y = log to the base 2( x ) ... the 2 is the base

(read as "log to the base 2 of x.")

That's it!  Logarithms are just inverses of exponentials!

So...  What's the inverse of this?

y = 3^( x )

Easy!

The inverse of y = 3^( x )isy = log to the base 3( x ).