Evaluate- 1-logxy xyz-1-logyz xyz-1-logzx xyz

1/log_xy xyz+1/log_yz xyz+1/log_zx xyz= =log_xyz xy+log_xyz yz+log_xyz xz nbsp; nbsp; nbsp;[∵1/log_a b=log_b a] nbsp;(0.5 Marks) =log_xyz x^2y^2z^2 ...

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Byju's Answer

Standard XIII

Mathematics

Fundamental Laws of Logarithms

Evaluate: 1/l...

Question

Evaluate: $\frac{1}{l o g_{x y} x y z} + \frac{1}{l o g_{y z} x y z} + \frac{1}{l o g_{z x} x y z}$

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Solution

$\frac{1}{l o g_{x y} x y z} + \frac{1}{l o g_{y z} x y z} + \frac{1}{l o g_{z x} x y z} =$

= $l o g_{x y z} x y + l o g_{x y z} y z + l o g_{x y z} x z$ $[∵ \frac{1}{l o g_{a} b} = l o g_{b} a]$ $(0.5 M a r k s)$

$= l o g_{x y z} x^{2} y^{2} z^{2}$ $∵ l o g_{a} m + l o g_{a} n = l o g_{a} m . n$ $(0.5 M a r k s)$

$= l o g_{x y z} {(x y z)}^{2}$ $(0.5 M a r k s)$

$= 2.1 = 2$ $(0.5 M a r k s)$

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Similar questions

Q. Evaluate:

\frac{1}{l o g_{x y} x y z} + \frac{1}{l o g_{y z} x y z} + \frac{1}{l o g_{z x} x y z} =

$\frac{1}{l o g_{x y} x y z} + \frac{1}{l o g_{y z} x y z} + \frac{1}{l o g_{z x} x y z} =$

Q. If

l o g_{x} y, l o g_{z} x, l o g_{y} z

are in G.P.,

x y z = 64

and

x^{3}, y^{3}, z^{3}

are in A.P., find

x + y + z

Q. Given

x^{3}, y^{3}, z^{3}

are in

A . P .

and

{l o g}_{x} y, {l o g}_{z} x, {l o g}_{y} z

are in

G . P .

x y z = 64

, then prove that

x = y = z = 4

Factorise the expression: z - 19 + 19 x y - x y z

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Evaluate: 1logxy xyz+1logyz xyz+1logzx xyz

1logxy xyz+1logyz xyz+1logzx xyz= =logxyz xy+logxyz yz+logxyz xz [∵1loga b=logb a] (0.5 Marks) =logxyz x2y2z2 ∵loga m+loga n=loga m.n (0.5 Marks) =logxyz (xyz)2 (0.5 Marks) =2.1=2 (0.5 Marks)

Evaluate: $\frac{1}{l o g_{x y} x y z} + \frac{1}{l o g_{y z} x y z} + \frac{1}{l o g_{z x} x y z}$