₂ (9-2^x )=10^ (3-x) , solve for x

Step-by-step solution

( aligned & Given, ₂ (9-2^x )=10^ ₁₀(3-x) & ₂ (9-2^x )=(3-x) [ a^ _a b =1 ] & 2^ 3-x =9-2^x & 2^3 2^x =9-2^x & 8=2^x (9-2^x ) & 2^ 2 x -2^x 9+8=0 aligned ) Let (2^x=y ), then ( aligned & y^2-9 y+8=0 & (y-8)(y-1)=0 & y=8 or y=1 & 2^x=2^3 or 2^x=2^ & x=3 or x=0 aligned ) But ( x =3 ) does not satisfy the given equation, since ( 0 ) is not defined.