Question

Question #93891

Answer 1

`x=2`

Explanation:

Your notation is very ambiguous. I am assuming the equation is
`3^(2x)-2*3^(x+2)+81=0`. If not, then this has all been in vain.
.....................................................................................................................................

`3^(2x)-2*3^(x+2)+81=0`

We can rewrite this using the laws of indices:

`3^(2x)=(3^x)^2`

`-2*3^(x+2)=-2*3^x*3^2`

So we have:

`(3^x)^2-2*3^x*3^2+81=0`

Simplify:

`(3^x)^2-18*3^x+81=0`

This is a quadratic in `3^x`

Let `u=3^x`

Then:

`u^2-18u+81=0`

Factor:

`(u-9)^2=0=>u=9`

But:

`u=3^x=>3^x=9`

`3^x=3^2=>x=2`