Question

The number of positive integers satisfying the equation x + log₁₀ (2^x + 1) = x log₁₀5 +log₁₀6 is

• A. 0
• B. 1
• C. 2
• D. Infinite

Answer 1

Answer: (B)

1

Answer 2

x[1 – log₁₀5] + log₁₀ (2^x + 1) = log₁₀6

x[log₁₀10 – log₁₀5] + log₁₀ (2^x + 1) = log₁₀6

x log₁₀2 + log₁₀ (2^x + 1) = log₁₀6

log₁₀2^x (2^x + 1) = log₁₀6

(2^x)² + 2^x – 6 = 0

2^x = 2 2^x = – 3

x = 1, which is not possible

+ve integer