If x^y = e^{x– y}, prove that

FORMULA:-

(i) logx^a = alogx

(ii) The quotient rule

(iii)loga+logb = log(a.b)

(iv)log_ee = 1

(v)

GIVEN:-

Taking log of both sides​

⇒log x^{y =} log e^{(x - y)}

Using formula (i)

y.logx = (x-y)loge

Using formula (iv)

y.logx = x-y

ylogx+y = x

Using formula (ii)

Using formula (v)