find the value of x^(logy-logz) × y^(logz-logx) ×z^(logx-logy)? pls answer this question now this making a brainliest answer tenn
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Step-by-step explanation:
Given :-
x^(log y-log z) × y^(log z - log x) × z^(log x-log y)
To find :-
Find the value of the expression ?
Solution :-
Given that :
x^(log y-log z) × 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
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