Question

The non-zero root of the equation $3^{2x}+9={10.3}^x$ is:

• A. a positive fraction
• B. a negative fraction
• C. a positive integer
• D. a negative integer

Answer 1

The correct option is C a positive integer

Given equation is: $3^{2x}+9=10.3^x$

Let $3^x=t$
Hence, $t^2+9=10t$
$t^2-10t+9=0$
$t^2-9t-t+9=0$
$t(t-9)-1(t-9)=0$
$(t-1)(t-9)=0$
$t=1$ and $t=9$
Hence, $3^x=1$
$x=0$ and $3^x=3^2$
$\therefore x=2$.