Solve the algebraic expression

Question

Solve $$8^ x +7\cdot 2^{x+1} = 7\cdot 4^x +8.$$

What's the best way to do this? Would I like convert to same indices?

Answer 1

Hint: I guess you mean $8^x+7 \cdot 2^x+1=7 \cdot 4^x +8$.

If so, put $y=2^x$. Then $y^3+7\cdot y +1 = 7y^2+8$.