Question

what is the answer of this equation?
a^(2x)-2(a^x)=15

Answer 1

\(\large a^{2x}-2a^x=15\)
Let \(\large t=a^x\) we have:
\(\large t^2-2t-15=0 \Rightarrow \begin{cases}t_1=5\\ t_2=-3 \end{cases}\)

\(\large \color{red}{t_1=5} \Rightarrow a^x=5 \Rightarrow x=log_{a}{5}\)
\(\large \color{red}{t_2=-3}\Rightarrow a^x=-3\Rightarrow x=log_{a}{-3}\)