What is expand ln((x^3y^2)/(z^5)) ?

The solution to expand ln((x^3y^2)/(z^5)) is 3ln(x)+2ln(y)-5ln(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ln((x^3y^2)/(z^5))

expand

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

3 ln (x) + 2 ln (y) - 5 ln (z)

Solution steps

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

Apply log rule:

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

ln (\frac{x ^{3} y ^{2}}{z ^{5}}) = ln (x^{3} y^{2}) - ln (z^{5})

= ln (x^{3} y^{2}) - ln (z^{5})

Apply log rule:

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

ln (z^{5}) = 5 ln (z)

= ln (x^{3} y^{2}) - 5 ln (z)

Apply log rule:

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

ln (x^{3} y^{2}) = ln (x^{3}) + ln (y^{2})

= ln (x^{3}) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

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

= 3 ln (x) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

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

= 3 ln (x) + 2 ln (y) - 5 ln (z)

ln (2 a) - ln (a)

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

lo g_{10} (x) + 5 lo g_{10} (y) - 4 lo g_{10} (z)

2 ln (x) - \frac{1}{2} ln (y)

lo g_{2} (\frac{x ^{2}}{x - 1})

What is expand ln((x^3y^2)/(z^5)) ?
The solution to expand ln((x^3y^2)/(z^5)) is 3ln(x)+2ln(y)-5ln(z)