High school math student here. In my homework I was asked to solve $16^x +4^{x+1} - 3= 0$ and I used substitution to get $x=\log_4{(-2+\sqrt7)}$. However, this was in the chapter on logarithms. How can I solve this without recourse to the quadratic formula etc, that is, using only logarithms and their properties and exponential functions and their properties? If I can't, how would one prove this is impossible?
2026-04-05 22:16:34.1775427394
Solving an exponential equation without the quadratic formula
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