If x log10 1 2x xlog10 5 log10 6 then x is equal to ........

Mathematics (NDA) Logarithm

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If, x + log₁₀ (1 + 2x) = xlog₁₀5 + log₁₀6

then x is equal to-

2,3

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Explanation:

x + log₁₀ (1+ 2^x) = x log₁₀5 + log₁₀6
Or x (1- log₁₀ 5) = log₁₀ 6 – log₁₀ (1+2^x)
Or x (log₁₀ 10 – log₁₀ 5) = log₁₀ (6/1+2^x)
X log₁₀ 2 = log₁₀ (6/1+2^x)
⇒ 2x =6/1+2^x
Or 2^x+ 2^2x = 6
Or 2^x (1 + 2^x) = 2(1+2)
By comparing, x = 1