Solve 9^x - 24(3^x) - 81 = 0 for the real value of x.
Answer and explanation
Correct answer: B. 3
- Step 1: Let t = 3^x, so the equation becomes t^2 - 24t - 81 = 0. Step 2. Factorise: (t - 27)(t + 3) = 0, so t = 27 or t = -3. Step 3. 3^x is always positive, so t = 27 and x = 3. Answer: 3. Why not the others: 27: That is the value of 3^x, not of x. -3: That is the other root for 3^x, which is negative and impossible. 4: That is one more than the correct exponent.
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