What is ln((x^2(3-x)^{2/3})/(sqrt(x^2+x+1))) ?

The solution to ln((x^2(3-x)^{2/3})/(sqrt(x^2+x+1))) is 2ln(x)+2/3 ln(3-x)-ln(sqrt(x^2+x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^2(3-x)^{2/3})/(sqrt(x^2+x+1)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

π (512 (ln (\frac{7}{2}) - ln (\frac{3}{2})) - \frac{5993}{15})

5 lo g_{7} (a) - 2 lo g_{7}^{b} (x)

ln (1.6 \cdot π)

3 lo g_{e} (2) + 5 lo g_{e} (π) - lo g_{e} (9)

lo g_{10} (A \cdot e^{- \frac{q}{r}})

What is ln((x^2(3-x)^{2/3})/(sqrt(x^2+x+1))) ?
The solution to ln((x^2(3-x)^{2/3})/(sqrt(x^2+x+1))) is 2ln(x)+2/3 ln(3-x)-ln(sqrt(x^2+x+1))