Question

the value of x^(logy-logz) × y^(logz-logx) ×z^(logx-logy)? I will post pic if u want​

Answer 1

Step-by-step explanation:

Given :-

x^(log y-log z)×y^(log z-logx)×z^(logx-log y)

To find :-

Find the value of the expression ?

Solution :-

Given that :

x^(logy-logz)×y^(log z-log x)×z^(log x-log y)

We know that

e^log a = a

On applying it to the above expression then

=> e^log [x^(log y-log z) × y^(log z - log x) × z^(log x-log y) ]

we know that

log ab = log a× log b

=> e^logx^(log y-log z)+log y^(log z - log x)

+ log z^(log x-log y) ]

We know that

log a^m = m log a

=> e^[{(logy-logz)logx}+ {(logz-logx)logy} + {(logx-logy)logz}]

=>e^[logxlogy-logxlogz+logylogz-logxlogy +logxlogz-logylogz]

=> e^0

=> 1

Answer:-

The value of the given expression is 0

Used formulae:-

→ e^log a = a

→ log ab = log a× log b

→ log a^m = m log a

→ e^0 = 1