Expand the logarithm logb squareroot 5774 12 logb 57 12logb

Expand the logarithm log_b squareroot 57/74 1/2 log_b 57 + 1/2log_b 74 1/2 log_b 57 - 1/2 log_b 74 squareroot log_b 57 - 1/2 log_b 74 log_b 1/2(57 - 74)

Solution

log(a/b) = log(a) - log(b)

log a^m = m loga

so apply these rules

log sqrt(a) = (1/2 )log a

logbsqrt [(57 / 74)] = 1/2 [ logb(57) - logb(74) ]

Answer is B)