If f(x) = log10 (1 + x), then what is 4f(4) + 5f(1) – log10 2 equal to?

If f(x) = log10 (1 + x), then what is 4f(4) + 5f(1) – log10 2 equal to? Correct Answer 4

Calculation:

Given: f(x) = log₁₀ (1 + x)

⇒ f(4) = log₁₀ (5)

⇒ f(1) = log₁₀ (2)

⇒ 4f(4) + 5f(1) – log₁₀ 2 = log₁₀ 625 + log₁₀ 32 - log₁₀ 2

⇒ 4f(4) + 5f(1) – log₁₀ 2 = log₁₀ (625 × 32) - log₁₀ 2

⇒ 4f(4) + 5f(1) – log₁₀ 2 = log₁₀ (2 × 10⁴) - log₁₀ 2

⇒ 4f(4) + 5f(1) – log₁₀ 2 = log₁₀ 2 + 4 log₁₀ 10 - log₁₀ 2

⇒ 4f(4) + 5f(1) – log₁₀ 2 = 4

Feb 20, 2025

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