Question

Given that log 2=0.3010 and log 3=0.4771, calculate without using mathematical tables or calculators, the values of

(A) log 54
(B) log 2.4
(C) log 30
(D) log 540

Answer 1

[AI-generated answer — Bot]

(A) log 54 = log (2 x 3^3) = log 2 + 3 log 3 = 0.3010 + 3(0.4771) = 1.7323

(B) log 2.4 = log (24/10) = log 24 - log 10 = log (2^3 x 3) - 1 = 3log2 + log3 - 1 = 3(0.3010) + 0.4771 - 1 = 0.3808
(C) log 30 = log (3 x 10) = log 3 + log 10 = log 3 + 1 = 0.4771 + 1 = 1.4771
(D) log 540 = log (54 x 10) = log 54 + log 10 = 1.7323 + 1 = 2.7323