CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If 2^x + 2^(x+2) = 80, the value of x is:
x equals 4. Rewrite 2^(x+2) as 4 × 2^x, so the equation becomes 5 × 2^x = 80, giving 2^x = 16 and x = 4. Checking: 2^4 + 2^6 = 16 + 64 = 80, which matches.
- A3
- B5
- C4Correct
- D2
Explanation
2^(x+2) = 4 × 2^x, so the left side is 2^x(1+4) = 5 × 2^x. Then 2^x = 16, so x = 4. Check: 16 + 64 = 80. Option 3 would give 8 + 32 = 40, and treating the sum as 2^(2x+2) is the mistake leading to other values.
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