3^2^x=1/243

Solution for 3^2^x=1/243 equation:

3^2^x=1/243

We move all terms to the left:

3^2^x-(1/243)=0

We add all the numbers together, and all the variables

3^2^x-(+1/243)=0

We get rid of parentheses

3^2^x-1/243=0

We multiply all the terms by the denominator


3^2^x*243-1=0

Wy multiply elements

729x^2-1=0

a = 729; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·729·(-1)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*729}=\frac{-54}{1458}
=-1/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*729}=\frac{54}{1458}
=1/27
$