en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(9)+2ln(4)

Solution

simplify

ln (9) + 2 ln (4)

Solution

2 ln (12)

+1

Solution steps

ln (9) + 2 ln (4)

Apply log rule:

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

2 ln (4) = ln (4^{2})

= ln (9) + ln (4^{2})

Apply log rule:

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

ln (9) + ln (4^{2}) = ln (4^{2} \cdot 9)

= ln (4^{2} \cdot 9)

9 \cdot 4^{2} = 144

= ln (144)

Rewrite

144

in power-base form:

144 = 1 2^{2}

= ln (1 2^{2})

Apply log rule:

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

ln (1 2^{2}) = 2 ln (12)

= 2 ln (12)

Popular Examples

simplify ln(9)+2ln(2)simplify

ln (9) + 2 ln (2)

simplify 4ln(3)+ln(2^6)simplify

4 ln (3) + ln (2^{6})

simplify-log_{10}(3.27*10^{-8})simplify

- lo g_{10} (3.27 \cdot 1 0^{- 8})

simplify-ln(-yln(1-ρ))simplify

- ln (- y ln (1 - ρ))

simplify ln(x)-1/2 ln(1+y^2)simplify

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

Frequently Asked Questions (FAQ)

What is ln(9)+2ln(4) ?
The solution to ln(9)+2ln(4) is 2ln(12)