Question

If aˣ=b, bʸ=c, cᶻ=a, then xyz= *

Answer 1

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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 2

Answer:

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