Question

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 25

Answer 1

We know that log 2 = 0.3010 and log 3 = 0.4771
log 25
= log`( 25/4 xx 4 )`
= log`( 100/4 )`           ...`[ log_a mn = log_a m + log_a n ]`
= log 100 - log( 2 x 2 )   ...`[ log_a (m/n) = log_a m - log_a n ]`
= 2 - log(2²)                   ...[ log 100 = 2 ]
= 2 - 2log2                     ...`[ log_a m^n = nlog_a m ]`
= 2 - 2( 0.3010 )             ...[ ∵ log 2 = 0.3010 ]
= 1.398