To solve this equation, you can first rewrite it as a quadratic equation in terms of (3^(2x)).
Let (y = 3^(2x)), the equation becomes((y - 1)(y^2 + y + 1) = 26)
Expanding the left side, we get(y^3 + y^2 + y - y^2 - y - 1 = 26)
Simplify(y^3 - 1 = 26)
Now, we can rewrite this equation back in terms of (3^(2x))(3^(2x)^3 - 1 = 26)
((3^(2x))^3 = 27)
(3^(6x) = 27)
(3^(6x) = 3^3)
Since the bases are the same, we can equate the exponents(6x = 3)
(x = 1/2)
Therefore, the solution to the equation is (x = 1/2).
To solve this equation, you can first rewrite it as a quadratic equation in terms of (3^(2x)).
Let (y = 3^(2x)), the equation becomes
((y - 1)(y^2 + y + 1) = 26)
Expanding the left side, we get
(y^3 + y^2 + y - y^2 - y - 1 = 26)
Simplify
(y^3 - 1 = 26)
Now, we can rewrite this equation back in terms of (3^(2x))
(3^(2x)^3 - 1 = 26)
((3^(2x))^3 = 27)
(3^(6x) = 27)
(3^(6x) = 3^3)
Since the bases are the same, we can equate the exponents
(6x = 3)
(x = 1/2)
Therefore, the solution to the equation is (x = 1/2).