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

$l o g_{a} c$ = $l o g_{b} a$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$l o g_{b} a$ = $l o g_{c} b$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$l o g_{c} b$ = $l o g_{a} c$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$l o g_{b} a$ = $l o g_{c} b$

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 $\frac{y}{x}$ = $\frac{z}{y}$

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

Suggest Corrections

Similar questions

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

x, y, z

G . P

a^{x} = b^{y} = c^{z}

a^{x} = b^{y} = c^{z}

a^{x} = b^{y} = c^{z}

a, b, c

x, y, z

a^{x} = b^{y} = c^{z} = d^{u}

a, b, c, d

x, y, z, u

Join BYJU'S Learning Program