Logarithms!

Logarithms are fascinating, and exponential math is certainly a favorite of mine. I think your confusion might derive from a misconception. Let us define notation: "^x" will denote an exponent, and logarithms will be written as "log(b,y)" (that is, log base 'b' of 'y'). If we write an exponent as y=b^x, its corresponding logarithm would be x=log(b,y), which is equivalent to writing (y=b^x)^-1 (the inverse). Now, a logarithm, like an exponent, has no value without a base... 3^2=9, but ^2 has no value, as nothing is being multiplied. So, if we take the inverse of (3^2=9), which is (2=log(3,9)), and remove the base, 3, (2=log(_,9)), we find an invalid logarithm; this has no value.

Or perhaps you are confused by the implied base 10 convention of logs:
The inverse of (100=10^2) is (2=log(10,100)), which can be simplified to (2=log100). Here, the base 10 of the log is implied, but is not missing.

I hope this has helped!

Virgil