The number of solutions of $\log _2\left(9-2^x\right)=10^{\log _{10}(3-x)}$ is

Question

Professor PC Thomas Classes · Answer

$\log_2(9-2^x) = 3-x \implies 9-2^x = 2^{3-x} = 8/2^x$. Let $2^x=y$. $y^2 - 9y + 8 = 0 \implies y=1,8 \implies x=0,3$.