Question

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 3.6

Answer 1

We know that log 2 = 0.3010 and log 3 = 0.4771.
log 3.6
= log`36/10`
= log 36 - log 10       ...`[ log_a (m/n) = log_a m - log_a n ]`
= log 2 x 2 x 3 x 3 - 1    ...[ ∵ log 10 = 1 ]
= log 2 x 2 + log 3 x 3 - 1  ...`[ log_a mn = log_a m + log_a n ]`
= log 2² + log 3² - 1    ]
= 2log2 + 2log3 - 1             ...`[ nlog_a m = log_a m^n ]` 
= 2(0.3010) + 2(0.4771) - 1
= 1.5562 - 1                       ...`[ ∵ log2 = 0.3010 and log 3 = 0.4771 ]`
= 0.5562