2^x*3^x=16384

Solution for 2^x*3^x=16384 equation:

2^x*3^x=16384

We move all terms to the left:

2^x*3^x-(16384)=0

Wy multiply elements

6x^2-16384=0

a = 6; b = 0; c = -16384;
Δ = b2-4ac
Δ = 02-4·6·(-16384)
Δ = 393216
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:

$\sqrt{\Delta}=\sqrt{393216}=\sqrt{65536*6}=\sqrt{65536}*\sqrt{6}=256\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-256\sqrt{6}}{2*6}=\frac{0-256\sqrt{6}}{12}
=-\frac{256\sqrt{6}}{12}
=-\frac{64\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+256\sqrt{6}}{2*6}=\frac{0+256\sqrt{6}}{12}
=\frac{256\sqrt{6}}{12}
=\frac{64\sqrt{6}}{3}
$