How to solve this equation with parameters on power?

How to solve this equation with parameters on power?

Please let me know how to solve this equation:
$$100^{1-b}=\frac{1}{2}40^{1-b}+\frac{1}{2}200^{1-b}$$
I try to use the trick of $x=e^{\log x}$ But it doesn't work
And $b\not=1$