Solve the equation log₉ x + log₉ ( x - 24)= 2. A)x = 29 B)x = -3 C)x = 27 D)x = 3 E)x = 729

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the two log terms on the left side because they have the same base (9) and are being added. This allows us to use the property log_b(a) + log_b(c) = log_b(a*c). So, we get log_9(x(x - 24)) = 2. To solve for x, we rewrite the equation in exponential form: 9^2 = x(x - 24). Simplifying, we get 81 = x^2 - 24x. Rearranging, we have x^2 - 24x - 81 = 0. Solving this quadratic equation, we find that x = 27 or x = -3. However, since x = -3 would result in taking the logarithm of a negative number, which is not possible in the real number system, the correct answer is x = 27.

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