What is ln(e/(xy))-e^{xy} ?

The solution to ln(e/(xy))-e^{xy} is 1-ln(x)-ln(y)-e^{xy}

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simplify ln(e/(xy))-e^{xy}

simplify

ln (\frac{e}{x y}) - e^{x y}

1 - ln (x) - ln (y) - e^{x y}

Solution steps

ln (\frac{e}{x y}) - e^{x y}

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e}{x y}) = ln (e) - ln (x y)

= ln (e) - ln (x y) - e^{x y}

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x y) = ln (x) + ln (y)

= ln (e) - (ln (x) + ln (y)) - e^{x y}

Apply log rule:

lo g_{a} (a) = 1

= 1 - (ln (x) + ln (y)) - e^{x y}

- (ln (x) + ln (y)) : - ln (x) - ln (y)

= 1 - ln (x) - ln (y) - e^{x y}

2 x + \frac{1}{2} ln (2 x + 1) - 3 ln (x + 2)

lo g_{8} ((x y^{2})^{2})

ln (\frac{4000}{500})

- \frac{1}{3 ln ^{2} ( 3 )}

\frac{6}{5} ln \frac{y}{x} - 1 + ln ∣ x ∣

What is ln(e/(xy))-e^{xy} ?
The solution to ln(e/(xy))-e^{xy} is 1-ln(x)-ln(y)-e^{xy}