Solve 9^x - 1(3^x) - 6 = 0 for the real value of x.
Answer and explanation
Correct answer: C. 1
- Step 1: Let t = 3^x, so the equation becomes t^2 - 1t - 6 = 0. Step 2. Factorise: (t - 3)(t + 2) = 0, so t = 3 or t = -2. Step 3. 3^x is always positive, so t = 3 and x = 1. Answer: 1. Why not the others: 3: That is the value of 3^x, not of x. -2: That is the other root for 3^x, which is negative and impossible. 2: That is one more than the correct exponent.
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