Question

If a^x=b ,b^y=c, c^z =a then prove that xyz=1

Answer 1

This question can be solved by applying log,
As
$log \: {m}^{n} = n \: log \: m$
So,
${a}^{x} = b \: \\ {b}^{y} = c \\ {c}^{z} = a$
Taking log both sides of the above equations,
$x \: log(a) = log(b) \\ y \: log(b) = log(c) \\ z \: log(c) = log(a)$
On multiplying the above equations,
$xyz \: = 1$
As log get cancelled out.

Hope it helped you!

Answer 2

Step-by-step explanation:

a can be written as ——a=10^log a

Similarly ——————- b= 10^log b

——————————— c= 10^log c

Where a,b,c are positive

(We know log of 10=1, log of 100=2, log of 1000=3

10 can be written as 10=(10 )^(log 10)

100 can be written as 100=( 10)^(log 100)

1000=(10)^(log 1000)

=10^3=1000 )

a^x=b

Now (10)^(log a )^x=10^log b

Since base is same (10),we can equate the exponents.

(log a)^x = log b

Or x log a =log b

Or x = (log b ) / (log a)

Similarly y=(log c)/(log b)

z =(log a) /( log c)

xyz =(log b)/(log a) X (log c)/(log b) X (log a)/( log c) = 1

xyz = 1 ANSWER.