If x- y- z are positive then minimum value ofx-log y-log z-y-log z-log x-z-log x-log y- is31916

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Toppr Admin · Accepted Answer

Let a-xlogy-x2212-logz-b-ylogz-x2212-logx-c-zlogx-x2212-logyNow- log-abc-loga-logb-logc-x21D2-log-abc-logy-x2212-logz-logx-logz-x2212-logx-logy-logx-x2212-logy-logz-0-x21D2-abc-1

If x, y, z are positive then minimum value of
$x^{log y - log z} + y^{log z - log x} + z^{log x - log y}$ is
$3$
$1$
$9$
$16$

Let $a = x^{l o g y - l o g z}, b = y^{l o g z - l o g x}, c = z^{l o g x - l o g y}$
Now, $l o g (a b c) = l o g a + l o g b + l o g c$
$\Rightarrow l o g (a b c) = (l o g y - l o g z) l o g x + (l o g z - l o g x) l o g y + (l o g x - l o g y) l o g z = 0$
$\Rightarrow a b c = 1$

If x, y, z are positive then minimum value ofxlogy−logz+ylogz−logx+zlogx−logy is31916

Let a=xlogy−logz,b=ylogz−logx,c=zlogx−logyNow, log(abc)=loga+logb+logc⇒log(abc)=(logy−logz)logx+(logz−logx)logy+(logx−logy)logz=0⇒abc=1

If x, y, z are positive then minimum value of
$x^{log y - log z} + y^{log z - log x} + z^{log x - log y}$ is
$3$
$1$
$9$
$16$

Let $a = x^{l o g y - l o g z}, b = y^{l o g z - l o g x}, c = z^{l o g x - l o g y}$
Now, $l o g (a b c) = l o g a + l o g b + l o g c$
$\Rightarrow l o g (a b c) = (l o g y - l o g z) l o g x + (l o g z - l o g x) l o g y + (l o g x - l o g y) l o g z = 0$
$\Rightarrow a b c = 1$