3^x*3^-5=81

Solution for 3^x*3^-5=81 equation:

3^x*3^-5=81

We move all terms to the left:

3^x*3^-5-(81)=0

We add all the numbers together, and all the variables

3^x*3^-86=0

Wy multiply elements

9x^2-86=0

a = 9; b = 0; c = -86;
Δ = b2-4ac
Δ = 02-4·9·(-86)
Δ = 3096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{86}}{2*9}=\frac{0-6\sqrt{86}}{18}
=-\frac{6\sqrt{86}}{18}
=-\frac{\sqrt{86}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{86}}{2*9}=\frac{0+6\sqrt{86}}{18}
=\frac{6\sqrt{86}}{18}
=\frac{\sqrt{86}}{3}
$