Question

11. If a^x= b, b^y= c and c^z= a, then value of xyz is:​

Answer 1

Step-by-step explanation:

Given:-

a^x= b, b^y= c and c^z= a

To find:-

Find the value of xyz ?

Solution:-

Given that

a^x = b-------(1)

b^y= c-----(2)

and c^z= a------(3)

On taking (3) equation

c^z = a

It can be written as

=> (b^y)^z = a (from (2))

We know that a^m×a^n = a^(m+n)

=> b^(yz)=a

And it can be written as

=> (a^x)^(yz)=a (from (1))

We know that a^m×a^n = a^(m+n)

=> a^xyz = a

=> a^xyz=a^1

On Comparing both sides then

xyz = 1

Answer:-

The value of xyz for the given problem is 1

Used formula:-

• a^m×a^n = a^(m+n)

• If bases are equal then exponents must be equal

Answer 2

Hey there!

a^x = b -------(1)

b^y = c -------(2)

c^z = a -------(3)

☞From equation (1) :

• a^x= b

(Taking log on both sides )

• log (a)^x = log b

• x log a =log b

• x = log b /log a

☞ from equation (2) :

• b^y = c

• log(b)^y = log c

• y log b = log c

• y = log c/ log b

☞ from equation (3) :

• c^z = a

• log (c)^z = log a

• z log c= log a

• z = log a /log c

Now multiplying x, y ,z :

= log b/loga . log c /log b . log a /log c

= 1

#Hope it helps !