Question

If x= log 5 7, y =log 7 27 , z =log 3 5, show that xyz = 3

Answer 1

Answer:

$xyz=3$

Step-by-step explanation:

Formula used:

Base changing rule:

$log_a{c}=(log_a{b})(log_b{c})$

Power rule:

$log_aM^n=n\:log_aM$

$log_a{a}=1$

Given:

$x=log_5{7}$

$y=log_7{27}$

$z=log_3{5}$

Now,

$xyz=(log_5{7})(log_7{27})(log_3{5})$

$xyz=(log_5{27})(log_3{5})$

$xyz=(log_5{3^3})(log_3{5})$

$xyz=3(log_5{3})(log_3{5})$

$xyz=3(log_5{5})$

$xyz=3(1)$

$xyz=3$

Hence proved.