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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5 ln (10) + 4 - 5 ln (5) + 1

ln (b c)

ln (x e^{y})

2 lo g_{a} (b) + 3 lo g_{a} (4 b)

4 lo g_{10} (a) - lo g_{10} (c)

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