# solve for y: $x = 1 - (1-y)^t$ [closed]

I have the following equation:

$$x = 1 - (1-y)^t$$

I would like to solve for $y$ in terms of $x$ and $t$. I tried WolframAlpha, but it did not generate a solution. Before you ask, yes this is a real problem, no this is not homework.

• $(1-y)^t=(1-x)$. So $1-y=(1-x)^{1/t}$. Aug 14, 2017 at 21:56
• Subtract both sides from $1$, then take logarithms of both sides. Whoops, that solves for $t$, never mind.
– MPW
Aug 14, 2017 at 21:56
• Logarithms are overkill, @MPW, though it works. Aug 14, 2017 at 21:57
• @ThomasAndrews : Yes, I thought he was after the exponent. My bad.
– MPW
Aug 14, 2017 at 21:57
• @ThomasAndrews this is the answer, thanks. My mind has forgotten how to get rid of the superscript and account for it on the other side. Aug 14, 2017 at 22:00

$$x = 1 - (1-y)^t$$ $$(1-y)^t=1-x$$ Notice that the following step does not always hold, for example if $t=2$, and $x>1$, we end up with no solution for $y$. But suppose every value is proper, we then have: $$\bigg( (1-y)^t \bigg)^{1/t}=(1-x)^{1/t}$$ $$1-y=(1-x)^{1/t}$$ $$-y=(1-x)^{1/t} -1$$ $$y=1-(1-x)^{1/t}$$