CDS 2025 · PYQ · Logarithms · medium
If log₁₀(100001 − 4^x)/(5 − x) = 1, then what is x equal to?
Answer
The correct answer is A: 0. Given log₁₀(100001 − 4^x)/(5 − x) = 1, so log₁₀(100001 − 4^x) = 5 − x. Thus 100001 − 4^x = 10^(5−x) = 100000/10^x.
- A.0✓ Correct
- B.1
- C.10
- D.100
Given log₁₀(100001 − 4^x)/(5 − x) = 1, so log₁₀(100001 − 4^x) = 5 − x. Thus 100001 − 4^x = 10^(5−x) = 100000/10^x. For x = 0: 100001 − 1 = 100000 ✓ and 10^(5−0) = 100000 ✓. So x = 0.
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