Determining the value of parameters given constraints If (x(y+z-x))/(log x)=(y(z+x-y))/(log y)=(z(x+y-z))/(log z) and ax^yy^x=by^zz^y=cz^xz^y then what is the value of a+b/c?

Alexander Lewis

Alexander Lewis

Answered question

2022-10-29

Determining the value of parameters given constraints
If
x ( y + z x ) log x = y ( z + x y ) log y = z ( x + y z ) log z
and
a x y y x = b y z z y = c z x z y
then what is the value of a + b c ?
I am getting as a x y y x = b y z z y = c z x x z after solving the first equation but according to the question it is not correct. So now I have to proove only that x z = z y , then my answer will be equal to 2.

Answer & Explanation

Kyle Delacruz

Kyle Delacruz

Beginner2022-10-30Added 21 answers

HINT:
x ( y + z x ) log x = y ( z + x y ) log y = z ( x + y z ) log z = m (say)
log x = x ( y + z x ) m         ( 1 )
and
a x y y x = b y z z y = c z x z y
log a + y log x + x log y = = n         ( 2 )(say)
Put the values of log x , log y , log z in ( 2 ) from ( 1 )

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