If x- y- z are in G-P- and a-x - nbsp-b-y - c-z- then -

The correct option is A x, y, z are in G.P., then y^2 = x.z Now nbsp;a^x = nbsp;b^y = c^z = m ⇒ x log_d nbsp;a = ylog_d nbsp;b = zlog_dc = log_dm ⇒ x ...

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Byju's Answer

Standard XII

Mathematics

Geometric Progression

If x, y, z ar...

Question

If x, y, z are in G.P. and $a^{x}$ = $b^{y}$ = $c^{z}$ , then

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Solution

The correct option is B

x, y, z are in G.P., then $y^{2}$ = x.z

Now $a^{x}$ = $b^{y}$ = $c^{z}$ = m

$\Rightarrow x l o g_{d} a$ = $y l o g_{d} b$ = $z l o g_{d} c$ = $l o g_{d} m$

$\Rightarrow x$ = $l o g_{a} m$ , y= $l o g_{b} m$ , z = $l o g_{c} m$

Again as x, y, z are in G.P., so $\frac{y}{x}$ = $\frac{z}{y}$

$\Rightarrow \frac{l o g_{b} m}{l o g_{a} m}$ = $\frac{l o g_{c} m}{l o g_{b} m}$ $\Rightarrow l o g_{b} a$ = $l o g_{c} b$

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If x, y, z are in G.P. and ax = by = cz, then

The correct option is B x, y, z are in G.P., then y2 = x.z Now ax = by = cz = m ⇒xlogda = ylogdb = zlogdc = logdm ⇒x = logam, y=logbm, z = logcm Again as x, y, z are in G.P., so yx = zy ⇒logbmlogam = logcmlogbm ⇒logba = logcb

If x, y, z are in G.P. and $a^{x}$ = $b^{y}$ = $c^{z}$ , then