What is 3x^2ysin(5x)-ln(4y) ?

The solution to 3x^2ysin(5x)-ln(4y) is 3x^2ysin(5x)-2ln(2)-ln(y)

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simplify 3x^2ysin(5x)-ln(4y)

simplify

3 x^{2} y sin (5 x) - ln (4 y)

3 x^{2} y sin (5 x) - 2 ln (2) - ln (y)

Solution steps

3 x^{2} y sin (5 x) - ln (4 y)

Apply log rule:

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

ln (4 y) = ln (4) + ln (y)

= 3 x^{2} y sin (5 x) - (ln (y) + ln (4))

ln (4) = 2 ln (2)

= 3 x^{2} y sin (5 x) - (ln (y) + 2 ln (2))

- (2 ln (2) + ln (y)) : - 2 ln (2) - ln (y)

= 3 x^{2} y sin (5 x) - 2 ln (2) - ln (y)

3 ln ∣ x - 2 ∣ + 4 ln ∣ x + 7 ∣

4.3 + lo g_{10} (\frac{0.02}{0.05})

\frac{1}{2} ln (x) + 8 ln (x^{3}) - 3 ln (x - 2)

lo g_{10} (25) + lo g_{10} (2) + lo g_{10} (0.02)

ln (\frac{0.017}{1})

What is 3x^2ysin(5x)-ln(4y) ?
The solution to 3x^2ysin(5x)-ln(4y) is 3x^2ysin(5x)-2ln(2)-ln(y)