Final answer:
To solve the equation (3² - 1 - 12 ⋅ 3ˣ⁺⁸¹ = 0), you can simplify and rewrite it as a quadratic equation. Then, divide both sides by -12 and take the logarithm of both sides. Finally, calculate the logarithms to find x ≈ -80.74.
Step-by-step explanation:
To solve the equation (3² - 1 - 12 ⋅ 3ˣ⁺⁸¹ = 0), we first simplify and rewrite it as a quadratic equation:
9 - 1 - 12⋅3ˣ⁺⁸¹ = 0
8 - 12⋅3ˣ⁺⁸¹ = 0
-12⋅3ˣ⁺⁸¹ = -8
Dividing both sides by -12, we get:
3ˣ⁺⁸¹ = 8/12
3ˣ⁺⁸¹ = 2/3
Taking the logarithm of both sides, we have:
(x+81)log(3) = log(2/3)
x+81 = log(2/3)/log(3)
x = log(2/3)/log(3) - 81
Calculating the logarithms, we find that x ≈ -80.74.