Solve Equation for x: R= ((a^-x)-(b^-x))/((c^-x)-(a^-x))

[physucsc11]

Homework Statement

To solve the following equation for x in terms of R and 3 constants a,b, and c:

R = ((a^-x)-(b^-x))/((c^-x)-(a^-x))

Homework Equations

Just the given equation

The Attempt at a Solution

I have tried taking the natural log of both sides but that doesn't seem to get me anywhere. Any suggestions?

 

[Mark44]

Your equation can be rewritten as
$$R = \frac{1/a^x - 1/b^x}{1/c^x - 1/a^x}$$

I would start with combining the two expressions in the numerator and the two in the denominator and simplify, then see where that takes me.