Density function of uniform prob distribution

Question

Let $X ∼\operatorname{Uniform}(0,1)$. Find the density function of $Y = e^X$.

I got to:

$F_Y(y)$=$P(Y\le y)$=$P(e^X\le y)$=$P(X\le \ln(y))$

Not sure where to go from here?

Answer 1

You are almost there, you have $$P(X\leq\ln(y))=F_X(\ln(y)),$$ where $F_X$ is the cumulative distribution function of $X$ ~ $U(0,1)$.