Question

If a^2=b^3=c^4=d^5 show that log bcd to the base a = 47/30

Answer 1

Answer:

From the given information

$b = a^\frac{2}{3} \\c = a^\frac{1}{2} \\d = a^\frac{2}{5} \\\\log_abcd = log_ab+log_ac+log_ad\\\\log_abcd = log_aa^\frac{2}{3} + log_aa^\frac{1}{2} + log_aa^\frac{2}{5}\\ \\= \frac{2}{3} + \frac{1}{2} + \frac{2}{5}  .............. [ log_aa^m = mlog_aa]\\\\=\frac{10(2)+15(1)+2(6)}{30} = \frac{47}{30}$