The value of (log3 5 x log25 27 x log49 7)/(log81 3) is

Question

 The value of \(\frac{log_3\,5\times\,log_{25}\,27\times\,log_{49}\,7}{log_{81}\,3}\) is

(a) 1 

(b) \(\frac{2}{3}\) 

(c) 3 

(d) 6

Answer 1

(c) 3

\(\frac{log_3\,5\times\,log_{25}\,27\times\,log_{49}\,7}{log_{81}\,3}\) = \(\frac{log_3\,5\times\,log_{5^2}\,3^3\times\,log_{7^2}\,7}{log_{3^4}\,3}\)

= \(\frac{log_3\,5\times\frac{3}{2}log_5\,3\times\frac{1}{2}log_7\,7}{\frac{1}{4}log_3\,3}\)

\(\bigg[\)Using log_aⁿ x^m = \(\frac{m}{n}\) log_a x, log_aⁿ x = \(\frac{1}{n}\) log_a x\(\bigg]\)

= 3 (log₃ 5 × log₅ 3) = 3 × 1 = 3 [Using log_b a × log_a b = 1]