Question

Given that log 2 = 0.3010 and log 3 = 0.4771, evaluate log√120 and leave your answer correct to four significant figure​

Answer 1

1.040

Explanation:

log √(120)

= (1/2) log 120

120 = 2³ • 3 • 5

= 0.5(3 log 2 + log 3 + log 5)

Express log 5 in terms of log 2.

log 5 = log (10/2) = log 10 - log 2 = 1 - log 2

= 0.5(3 log 2 + log 3 + 1 - log 2)

= 0.5(2 log 2 + log 3 + 1)

= 0.5(2*0.3010 + 0.4771 + 1)

= 1.03955 or 1.040