en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(3)+3ln(y)

Solution

simplify

3 ln (3) + 3 ln (y)

Solution

ln (27 y^{3})

Solution steps

3 ln (3) + 3 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

3^{3} = 27

= ln (27 y^{3})

Popular Examples

simplify log_{b}(y^5z)simplify

lo g_{b} (y^{5} z)

simplify log_{3}(m)+log_{3}(5)-log_{3}(n)simplify

lo g_{3} (m) + lo g_{3} (5) - lo g_{3} (n)

simplify 1/(log_{2)(10)+log_{2}(9)}simplify

\frac{1}{lo g _{2} ( 10 ) + lo g _{2} ( 9 )}

simplify log_{9}(8)-log_{9}(11)simplify

lo g_{9} (8) - lo g_{9} (11)

simplify log_{12}(a/b)simplify

lo g_{12} (\frac{a}{b})

Frequently Asked Questions (FAQ)

What is 3ln(3)+3ln(y) ?
The solution to 3ln(3)+3ln(y) is ln(27y^3)