What is ln((3x^2(1-x))/(16)) ?

The solution to ln((3x^2(1-x))/(16)) is ln(3)+2ln(x)+ln(1-x)-4ln(2)

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simplify ln((3x^2(1-x))/(16))

simplify

ln (\frac{3 x ^{2} ( 1 - x )}{16})

ln (3) + 2 ln (x) + ln (1 - x) - 4 ln (2)

Solution steps

ln (\frac{3 x ^{2} ( 1 - x )}{16})

Apply log rule:

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

ln (\frac{3 x ^{2} ( 1 - x )}{16}) = ln (3 x^{2} (1 - x)) - ln (16)

= ln (3 x^{2} (- x + 1)) - ln (16)

Apply log rule:

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

ln (3 x^{2} (1 - x)) = ln (3) + ln (x^{2}) + ln (1 - x)

= ln (3) + ln (x^{2}) + ln (- x + 1) - ln (16)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= ln (3) + 2 ln (x) + ln (1 - x) - ln (16)

ln (16) = 4 ln (2)

= ln (3) + 2 ln (x) + ln (- x + 1) - 4 ln (2)

lo g_{10} (\frac{sin ( x )}{x})

lo g_{x} (- 2 lo g_{10} (x - 1))

ln (\frac{1.81}{0.498})

ln (x - 68) - ln (x + 14)

1.6 \cdot ln (0.9 n)

What is ln((3x^2(1-x))/(16)) ?
The solution to ln((3x^2(1-x))/(16)) is ln(3)+2ln(x)+ln(1-x)-4ln(2)