What is ln(1/(xy))-e^{xy} ?

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

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simplify ln(1/(xy))-e^{xy}

simplify

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

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

Solution steps

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

Apply log rule:

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

ln (\frac{1}{x y}) = ln (1) - ln (x y)

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (y)) - e^{x y}

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

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

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

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

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