Question

If 16^x=13. what is the value of 2^2x+1

Answer 1

`16^x=13\implies (2^4)^x=13\implies ((2^2)^2)^x=13\implies ((4)^2)^x=13 \\\\\\ 4^(2\cdot x)=13\implies 4^(x\cdot 2)=13\implies \left[4^x \right]^2=13\implies \boxed{4^x}=√(13) \\\\[-0.35em] ~\dotfill\\\\ 2^(2x+1)\implies 2^(2x)\cdot 2^1\implies (2^2)^x\cdot 2\implies 4^x\cdot 2\implies \boxed{√(13)}\cdot 2\implies 2√(13)`