Question

1. 3^x+9.3^-x=10

Answer 1

\(3^x+9\cdot3^{-x}=10\)

=>\(3^x+\dfrac{9}{3^x}=10\)

=>\(\dfrac{\left(3^x\right)^2+9}{3^x}=10\)

=>\(\left(3^x\right)^2+9=10\cdot3^x\)

=>\(\left(3^x\right)^2-10\cdot3^x+9=0\)

=>\(\left(3^x-1\right)\left(3^x-9\right)=0\)

=>\(\left[{}\begin{matrix}3^x-1=0\\3^x-9=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}3^x=1\\3^x=9\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)