What is ln((x^2sqrt(x-4))/(4x+1)) ?

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

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simplify ln((x^2sqrt(x-4))/(4x+1))

simplify

ln (\frac{x ^{2} x - 4}{4 x + 1})

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

Solution steps

ln (\frac{x ^{2} x - 4}{4 x + 1})

Apply log rule:

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

ln (\frac{x ^{2} x - 4}{4 x + 1}) = ln (x^{2} x - 4) - ln (4 x + 1)

= ln (x^{2} x - 4) - ln (4 x + 1)

Apply log rule:

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

ln (x^{2} x - 4) = ln (x^{2}) + ln (x - 4)

= ln (x^{2}) + ln (x - 4) - ln (4 x + 1)

Apply log rule:

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

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

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

ln (\frac{x ^{4} x ^{2} + 2}{( x + 2 ) ^{9}})

0.52 \cdot ln (\frac{405.37}{451})

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

(ln (1) - ln (12)) + ln (M) + ln (L^{2})

- ln (2) + ln (7) - ln (6)

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