What is x^3y^3z^3+ln(y^5z^4) ?

The solution to x^3y^3z^3+ln(y^5z^4) is x^3y^3z^3+5ln(y)+4ln(z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify x^3y^3z^3+ln(y^5z^4)

simplify

x^{3} y^{3} z^{3} + ln (y^{5} z^{4})

x^{3} y^{3} z^{3} + 5 ln (y) + 4 ln (z)

Solution steps

x^{3} y^{3} z^{3} + ln (y^{5} z^{4})

Apply log rule:

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

ln (y^{5} z^{4}) = ln (y^{5}) + ln (z^{4})

= x^{3} y^{3} z^{3} + ln (y^{5}) + ln (z^{4})

Apply log rule:

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

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

= x^{3} y^{3} z^{3} + 5 ln (y) + ln (z^{4})

Apply log rule:

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

ln (z^{4}) = 4 ln (z)

= x^{3} y^{3} z^{3} + 5 ln (y) + 4 ln (z)

lo g_{7} (49 x yz)

2 lo g_{a} (9 x^{2}) - \frac{1}{6} lo g_{a} (7 x + 3)

lo g_{b} (m) - lo g_{b} (n)

lo g_{6} ((u^{2} v)^{4})

lo g_{6} (18 x)

What is x^3y^3z^3+ln(y^5z^4) ?
The solution to x^3y^3z^3+ln(y^5z^4) is x^3y^3z^3+5ln(y)+4ln(z)