en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

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

Solution

2 ln (72)

+1

Solution steps

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

Apply log rule:

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

4 ln (3) = ln (3^{4})

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

Apply log rule:

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

ln (3^{4}) + ln (2^{6}) = ln (2^{6} \cdot 3^{4})

= ln (2^{6} \cdot 3^{4})

3^{4} \cdot 2^{6} = 5184

= ln (5184)

Rewrite

5184

in power-base form:

5184 = 7 2^{2}

= ln (7 2^{2})

Apply log rule:

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

ln (7 2^{2}) = 2 ln (72)

= 2 ln (72)

Popular Examples

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})

simplify ln(uv^3)simplify

ln (u v^{3})

simplify 2ln(4)-ln(3)simplify

2 ln (4) - ln (3)

Frequently Asked Questions (FAQ)

What is 4ln(3)+ln(2^6) ?
The solution to 4ln(3)+ln(2^6) is 2ln(72)