Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[y=\frac{1}{{2}^{x-1}}+2\]
Subtract \(2\) from both sides.
\[y-2=\frac{1}{{2}^{x-1}}\]
Multiply both sides by \({2}^{x-1}\).
\[(y-2)\times {2}^{x-1}=1\]
Divide both sides by \(y-2\).
\[{2}^{x-1}=\frac{1}{y-2}\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[x-1=\log_{2}{(\frac{1}{y-2})}\]
Add \(1\) to both sides.
\[x=\log_{2}{(\frac{1}{y-2})}+1\]
x=log(2,1/(y-2))+1
