3^x*3^x=2187

Solution for 3^x*3^x=2187 equation:

3^x*3^x=2187

We move all terms to the left:

3^x*3^x-(2187)=0

Wy multiply elements

9x^2-2187=0

a = 9; b = 0; c = -2187;
Δ = b2-4ac
Δ = 02-4·9·(-2187)
Δ = 78732
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:

$\sqrt{\Delta}=\sqrt{78732}=\sqrt{26244*3}=\sqrt{26244}*\sqrt{3}=162\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162\sqrt{3}}{2*9}=\frac{0-162\sqrt{3}}{18}
=-\frac{162\sqrt{3}}{18}
=-9\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162\sqrt{3}}{2*9}=\frac{0+162\sqrt{3}}{18}
=\frac{162\sqrt{3}}{18}
=9\sqrt{3}
$