Subtract \(\frac{1}{1+{x}^{b-9}}\) from both sides.
\[\frac{1}{1+{x}^{a-b}}=1-\frac{1}{1+{x}^{b-9}}\]
Multiply both sides by \(1+{x}^{a-b}\).
\[1=(1-\frac{1}{1+{x}^{b-9}})(1+{x}^{a-b})\]
Divide both sides by \(1-\frac{1}{1+{x}^{b-9}}\).
\[\frac{1}{1-\frac{1}{1+{x}^{b-9}}}=1+{x}^{a-b}\]
Subtract \(1\) from both sides.
\[\frac{1}{1-\frac{1}{1+{x}^{b-9}}}-1={x}^{a-b}\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[\log_{x}{(\frac{1}{1-\frac{1}{1+{x}^{b-9}}}-1)}=a-b\]
Add \(b\) to both sides.
\[\log_{x}{(\frac{1}{1-\frac{1}{1+{x}^{b-9}}}-1)}+b=a\]
Switch sides.
\[a=\log_{x}{(\frac{1}{1-\frac{1}{1+{x}^{b-9}}}-1)}+b\]
a=log(x,1/(1-1/(1+x^(b-9)))-1)+b
