Question

If + log₁₀(1 + 2) = log₁₀5+ log₁₀ 6 then is equal to 

A. 2, 3 

B. 2 only 

C. 1 

D. 3

Answer 1

Correct option   C. 1

Explanation:

x + log₁₀ (1 + 2^x) = x log₁₀ 5 + log₁₀ 6 

Or x (1- log₁₀ 5) = log₁₀ 6 – log₁₀ (1+ 2^x) 

Or x (log₁₀10 – log₁₀5) = log₁₀ (6/1 + 2) 

X log₁₀ 2 = log₁₀ ( 6/1+2) 

⇒ 2^x = 6/1+2 

Or 2^x + 2^2x = 6 

Or 2^x (1 + 2^x) = 2(1 + 2) 

By comparing, x = 1