What is 2ln(x)-4log_{e}(1/y)-3log_{e}(x)y ?

The solution to 2ln(x)-4log_{e}(1/y)-3log_{e}(x)y is 2ln(x)+4ln(y)-3yln(x)

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simplify 2ln(x)-4log_{e}(1/y)-3log_{e}(x)y

simplify

2 ln (x) - 4 lo g_{e} (\frac{1}{y}) - 3 lo g_{e} (x) y

2 ln (x) + 4 ln (y) - 3 y ln (x)

Solution steps

2 ln (x) - 4 lo g_{e} (\frac{1}{y}) - 3 lo g_{e} (x) y

Apply log rule:

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

lo g_{e} (\frac{1}{y}) = lo g_{e} (1) - lo g_{e} (y)

= 2 ln (x) - 4 (- lo g_{e} (y) + lo g_{e} (1)) - 3 y lo g_{e} (x)

4 (lo g_{e} (1) - lo g_{e} (y)) = - 4 ln (y)

3 lo g_{e} (x) y = 3 y ln (x)

= 2 ln (x) - (- 4 ln (y)) - 3 y ln (x)

Apply rule

- (- a) = a

= 2 ln (x) + 4 ln (y) - 3 ln (x) y

3 ln (5) - \frac{1}{2} ln (4) + ln (8)

lo g_{4} (\frac{4 a}{b})

10.64 + lo g_{10} (\frac{0.13}{0.25})

- (ln (x + 1) + ln (x + 2))

ln (\frac{16.9 \cdot 1 0 ^{3}}{80})

What is 2ln(x)-4log_{e}(1/y)-3log_{e}(x)y ?
The solution to 2ln(x)-4log_{e}(1/y)-3log_{e}(x)y is 2ln(x)+4ln(y)-3yln(x)