What is ln((x^3sqrt(x-1))/(3x+4)) ?

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

Popular >

simplify ln((x^3sqrt(x-1))/(3x+4))

simplify

ln (\frac{x ^{3} x - 1}{3 x + 4})

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

Solution steps

ln (\frac{x ^{3} x - 1}{3 x + 4})

Apply log rule:

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

ln (\frac{x ^{3} x - 1}{3 x + 4}) = ln (x^{3} x - 1) - ln (3 x + 4)

= ln (x^{3} x - 1) - ln (3 x + 4)

Apply log rule:

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

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

= ln (x^{3}) + ln (x - 1) - ln (3 x + 4)

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

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

lo g_{10} (\frac{x ^{3}}{z y ^{4}})

lo g_{3} (\frac{x}{x ^{2}})

lo g_{3} (7 x) - lo g_{3} (7 y)

lo g_{10} (\frac{8 c}{10})

lo g_{10} (0.5) + lo g_{10} (\frac{1}{2})

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