The value of log √b a log cube root (c) b log 4√a c is:

Question

The value of log_√b a \(\text{log}_\sqrt[3]{c}\)  b \(\text{log}_\sqrt[4]{c}\) c is:

(a) 1 

(b) 10 

(c) 24 

(d) 0

Answer 1

(c) 24

Using the formula log_aⁿ x^m = \(\frac{m}{n}\) log_a x , we have

 log_√b a \(\text{log}_\sqrt[3]{c}\)  b \(\text{log}_\sqrt[4]{c}\) c = \(\text{log}_{b^\frac{1}{2}}\) a \(\text{log}_{c^\frac{1}{3}}\) b \(\text{log}_{a^\frac{1}{4}}\)c

= 2 log_b^a × 3 log_c^b × 4 log_a^c

= 24 \(\frac{log\,a}{log\,b}\times\frac{log\,b}{log\,c}\times\frac{log\,c}{log\,a}\) = 24.