Question

${\large{\underline{\underline{\pmb{\frak{Question:-}}}}}}$
Find the value of m if $\sf \;\; m = (yz)^{logy-logz} \times (zx)^{logz-logx} \times (xy)^{logx-logy}$

Answer 1

Answer:

Let : 

K = [(yz)^(log y - log z)] • [(zx)^(log z - log x)] • [(xy)^(log x - log y)] 

Then : 

log K = (log y - log z)· log (yz) + ... two similar terms 

. . . . = (log y - log z)·(log y + log z) + ... two similar terms 

. . . . = [ (log y)² - (log z)² ] + [ (log z)² - (log x)² ] + [ (log x)² - (log y)² ] 

. . . . = 0. 

Since : log K = 0, 

Hence : K = 1. 

Thus, the result is proved. 

Answer 2

$)^{logy-logz} \times (zx)^{logz-logx} \times (xy)^{logx-logy}$[/tex]