   SEARCH HOME Math Central Quandaries & Queries  Question from keith, a student: please help me find the inverse of this function: h(t) = 2 + 4 ln(1-5t) if you could give me a detailed explanation of how to find the inverse review problem above before my finale exam tomorrow that would be helpful. thanks Hi Keith. The inverse of a ln function is an exponentiation (e) function. Here's my example a lot like your question:

f(t) = 5 - 3 ln(5t + 1)

So I "solve" for t. First I isolate the ln( ) function:
ln(5t + 1) = [5 - f] / 3

Now to eliminate the ln( ) part, I raise both sides as exponents of e:
e[ ln(5t + 1) ] = e[ (5 - f) / 3]

This makes the e and the ln cancel each other on the left side, dropping the 5t + 1 down:
5t + 1 = e[ (5 - f) / 3]

and I continue to isolate t in the usual way:
t = [ e[ (5 - f) / 3] - 1 ] / 5

Not a very pretty answer, but that is the inverse of f(t).

Now you try yours.
Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.