If $3^{x} = z, z^{y} = 5, 5^{z} = 3$ then $x y z = ?$

0

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

5

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

3

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

1

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

Open in App

Solution

The correct option is A $1$
$3^{x} = z$
$\Rightarrow x^{x y} = 5$ ...(i) $[∵ z^{y} = 5]$
and $5^{z} = 3$
So, $5 = 3^{\frac{1}{z}}$ ...(ii)
From equation (1) and (2)
$3^{x y} = 3^{\frac{1}{z}}$ (Compare both side)
$x y = \frac{1}{z}$
$\Rightarrow x y z = 1$
So, ans $(d)$ is correct

Suggest Corrections

Similar questions

If $x + y + z = 0$
then $x^{3} + y^{3} + z^{3}$ =___?

x + y + z = 0

\frac{x^{3} + y^{3}}{x y z} = \frac{y^{3} + z^{3}}{x y z} = \frac{x^{3} + z^{3}}{x y z} = a

\sqrt[3]{(1 - x^{3})} (y - z) + \sqrt[3]{(1 - y^{3})} (z - x) + \sqrt[3]{(1 - z^{3})} (x - y) = 0

(1 - x)^{3} (1 - y)^{3} (1 - z)^{3} = (1 - x y z)^{3}

x + y + z = x y z

\frac{3 x - x^{3}}{1 - 3 x^{2}} + \frac{3 y - y^{3}}{1 - 3 y^{2}} + \frac{3 z - z^{3}}{1 - 3 z^{2}} = \frac{3 x - x^{3}}{1 - 3 x^{2}} \cdot \frac{3 y - y^{3}}{1 - 3 y^{2}} \cdot \frac{3 z - z^{3}}{1 - 3 z^{2}}

∣ ∣ ∣ ∣ ∣ \begin{matrix} x & x^{2} & 1 + x^{3} y & y^{2} & 1 + y^{3} z & z^{2} & 1 + z^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

Join BYJU'S Learning Program