If x18-y21-z28 then 3-3 log y x- 3 log 2 y- 7 log x z are in

The correct option is A A.P.Let x^18=y^21=z^28=k, then 18 log x=21 log y=28 log z=log k Now 3log_Y X=3log x/log y=3.21/18=7/2 3log_z y=3.28/21=4, 7log_x z=7.18 ...

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Byju's Answer

Standard IX

Mathematics

Fundamental Laws of Logarithms

If x18=y21=z2...

Question

If $x^{18} = y^{21} = z^{28} t h e n 3, 3 l o g_{y} x, 3 l o g_{z} y, 7 l o g_{x} z$ are in

A.P.

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G.P.

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H.P.

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None

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Solution

The correct option is A A.P.
Let $x^{18} = y^{21} = z^{28} = k$ , then
$18 l o g x = 21 l o g y = 28 l o g z = l o g k$
Now $3 l o g_{Y} X = 3 \frac{l o g x}{l o g y} = 3. \frac{21}{18} = \frac{7}{2}$
$3 l o g_{z} y = 3. \frac{28}{21} = 4, 7 l o g_{x} z = 7. \frac{18}{28} = \frac{9}{2}$
Hence the numbers are 3. $3 \frac{1}{2}$ , 4 and $4 \frac{1}{2}$ , which are clearly in A.P

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If x18=y21=z28then3,3logy x,3logz y,7logx z are in

The correct option is A A.P.Let x18=y21=z28=k, then 18logx=21logy=28logz=logk Now 3logY X=3log xlog y=3.2118=72 3logz y=3.2821=4,7logx z=7.1828=92 Hence the numbers are 3. 312, 4 and 412, which are clearly in A.P

If $x^{18} = y^{21} = z^{28} t h e n 3, 3 l o g_{y} x, 3 l o g_{z} y, 7 l o g_{x} z$ are in