Final answer:
To solve the equation 7²ˣ + 7ˣ - 12 = 0, we can use a substitution method. Let's substitute a variable, let's say y, for 7ˣ. The equation then becomes y² + y - 12 = 0. Solving this quadratic equation, we find the solutions x = log₇ 3 and x = log₇ (-4).
Step-by-step explanation:
To solve the equation 7²ˣ + 7ˣ - 12 = 0, we can use a substitution method. Let's substitute a variable, let's say y, for 7ˣ. The equation then becomes y² + y - 12 = 0. We can now solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation, we get (y - 3)(y + 4) = 0. This gives us two solutions: y = 3 and y = -4. Plugging in the value of y back into the original equation, we find that 7ˣ = 3 and 7ˣ = -4. Solving these equations, we get the solutions x = log₇ 3 and x = log₇ (-4), respectively.