# Solving $x$ for $y= 3^x-2^x$

Is there a way to solve for $x$ given the function: $$y= 3^x-2^x$$ in terms of $y$?

I tried a lot of algebraic manipulations but I ended up nothing. Or, should we say it it impossible to do so?

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It's $\rm\ Z^C - Z\: =\: Y\$ for $\rm\ Z = 2^X,\:\ C = log_2 3$. – Bill Dubuque Mar 9 '12 at 4:00
$x,y$ are what? Natural numbers? – GEdgar Mar 9 '12 at 4:07
any positive real numbers – Keneth Adrian Mar 9 '12 at 4:12

There is no expression for $x$ in closed form as an elementary function of $y$.