# Math Help - Find the domain of the following function

1. ## Find the domain of the following function

hello
it seems not easy
since we have base and exponent

$f(x)=(1-x)^{ln(2x+1)}$

2. The exponent is defined if and only if $2x+1>0$, i.e. $x>\frac{-1}{2}$
Additionally one needs $1-x>0$, $1-x=0$ and $ln(2x+1)>0$, Or, $1-x \neq 0$ and $ln(2x+1)=r$ where r is a rational number with odd denominato.
i.e. $x<1$, $x=1$, or $x=\frac{e^r-1}{2}$ with $r$ as stated.

Answer: $(\frac{-1}{2},1]$ U { $\frac{e^r-1}{2}$ : r is a rational number number with odd denominator}.