Question

if p^x = q, q^y =r, r^z = p^6 then the value of xyz is

a) 0
b) 1
c) 3
d) 6

Answer 1

p^x = q
& q^y = r
=> (p^x)^y = r
& r^z = p^6
=> {(p^x)^y}^z =p^6
=> p^xyz = p^6
comparing powers on both sides …
xyz = 6



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Answer 2

The value of xyz = 6

Given :

$\sf {p}^{x} = q \: , \: {q}^{y} = r \: , \: {r}^{z} = {p}^{6}$

To find :

The value of xyz is

a) 0

b) 1

c) 3

d) 6

Solution :

Step 1 of 2 :

Write down the given expression

Here it is given that

$\sf {p}^{x} = q \: , \: {q}^{y} = r \: , \: {r}^{z} = {p}^{6}$

Step 2 of 2 :

Find the value of xyz

$\sf {p}^{x} = q \: , \: {q}^{y} = r \: , \: {r}^{z} = {p}^{6}$

Now

$\sf {r}^{z} = {p}^{6}$

$\displaystyle \sf{ \implies } {( {q}^{y} )}^{z} = {p}^{6}$

$\displaystyle \sf{ \implies } {q}^{yz} = {p}^{6}$

$\displaystyle \sf{ \implies } {( {p}^{x} )}^{yz} = {p}^{6}$

$\displaystyle \sf{ \implies } {p}^{xyz} = {p}^{6}$

$\displaystyle \sf{ \implies } xyz = 6$

The value of xyz = 6

Hence the correct option is d) 6

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