What is ln((x^2)/(sqrt(x)(1+x)^5)) ?

The solution to ln((x^2)/(sqrt(x)(1+x)^5)) is 2ln(x)-ln(sqrt(x))-5ln(1+x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^2)/(sqrt(x)(1+x)^5))

simplify

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}})

2 ln (x) - ln (x) - 5 ln (1 + x)

Solution steps

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}})

Apply log rule:

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

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}}) = ln (x^{2}) - ln (x (1 + x)^{5})

= ln (x^{2}) - ln (x (x + 1)^{5})

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 (1 + x)^{5})

Apply log rule:

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

ln (x (1 + x)^{5}) = ln (x) + ln ((1 + x)^{5})

= 2 ln (x) - (ln (x) + ln ((x + 1)^{5}))

Apply log rule:

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

ln ((1 + x)^{5}) = 5 ln (1 + x)

= 2 ln (x) - (ln (x) + 5 ln (1 + x))

- (ln (x) + 5 ln (1 + x)) : - ln (x) - 5 ln (1 + x)

= 2 ln (x) - ln (x) - 5 ln (1 + x)

lo g_{2} (8 x y)

lo g_{\frac{1}{6}} (\frac{4}{9})

- \frac{6}{8} lo g_{2} (\frac{6}{8}) - \frac{2}{8} lo g_{2} (\frac{2}{8})

- lo g_{b} (\frac{1}{5})

What is ln((x^2)/(sqrt(x)(1+x)^5)) ?
The solution to ln((x^2)/(sqrt(x)(1+x)^5)) is 2ln(x)-ln(sqrt(x))-5ln(1+x)