Solve for h (complex solution)
\left\{\begin{matrix}h=-\frac{1-\left(\frac{1}{2}\right)^{x}}{y}\text{, }&y\neq 0\\h\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=-\frac{2\pi n_{1}i}{\ln(2)}\text{ and }y=0\end{matrix}\right.
Solve for h
\left\{\begin{matrix}h=-\frac{1-\left(\frac{1}{2}\right)^{x}}{y}\text{, }&y\neq 0\\h\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
x=-\log_{2}\left(hy+1\right)-\frac{2\pi n_{1}i}{\ln(2)}
n_{1}\in \mathrm{Z}
y=0\text{ or }h\neq -\frac{1}{y}
Solve for x
x=-\log_{2}\left(hy+1\right)
\left(h<-\frac{1}{y}\text{ and }y<0\right)\text{ or }y=0\text{ or }\left(h>-\frac{1}{y}\text{ and }y>0\right)
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yh=\left(\frac{1}{2}\right)^{x}-1
The equation is in standard form.
\frac{yh}{y}=\frac{\left(\frac{1}{2}\right)^{x}-1}{y}
Divide both sides by y.
h=\frac{\left(\frac{1}{2}\right)^{x}-1}{y}
Dividing by y undoes the multiplication by y.
yh=\left(\frac{1}{2}\right)^{x}-1
The equation is in standard form.
\frac{yh}{y}=\frac{\left(\frac{1}{2}\right)^{x}-1}{y}
Divide both sides by y.
h=\frac{\left(\frac{1}{2}\right)^{x}-1}{y}
Dividing by y undoes the multiplication by y.
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