Assuming that the base is 10, the value of the expression log 6 + 2 lo

1.	Assuming that the base is 10, the value of the expression log 6 + 2 log 5 + log 4 – log 3 – log 2 is(a) 0 (b) 1 (c) 2 (d) 3
Answer» (c) 2 Given exp. = log 6 + 2 log5 + log 4 – log 3 – log 2 = log 6 + log (5)² + log 4 – log 3 – log 2 = log 6 + log 25 + log 4 – (log 3 + log 2) = log (6 × 25 × 4) – log (3 × 2) = log \(\bigg(\frac{6\times25\times4}{3\times2}\bigg)\) = log₁₀ 100 = log₁₀ 10² = 2 log₁₀ 10 = 2 x 1 = 2.

Assuming that the base is 10, the value of the expression log 6 + 2 log 5 + log 4 – log 3 – log 2 is(a) 0 (b) 1 (c) 2 (d) 3

Answer»

(c) 2

Given exp. = log 6 + 2 log5 + log 4 – log 3 – log 2

= log 6 + log (5)² + log 4 – log 3 – log 2

= log 6 + log 25 + log 4 – (log 3 + log 2)

= log (6 × 25 × 4) – log (3 × 2)

= log \(\bigg(\frac{6\times25\times4}{3\times2}\bigg)\) = log₁₀ 100 = log₁₀ 10²

= 2 log₁₀ 10 = 2 x 1 = 2.