en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 12+4ln(9/5)

Solution

simplify

12 + 4 ln (\frac{9}{5})

Solution

12 + 4 (2 ln (3) - ln (5))

+1

Decimal Notation

14.35114 \dots

Solution steps

12 + 4 ln (\frac{9}{5})

Apply log rule:

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

ln (\frac{9}{5}) = ln (9) - ln (5)

= 12 + 4 (ln (9) - ln (5))

ln (9) = 2 ln (3)

= 12 + 4 (2 ln (3) - ln (5))

Popular Examples

expand log_{b}(x^3)y^5 expand

lo g_{b} (x^{3}) y^{5}

simplify ln(5)+ln(5^2)+ln(5^3)simplify

ln (5) + ln (5^{2}) + ln (5^{3})

simplify ln(x^2y^{1/3})simplify

ln (x^{2} y^{\frac{1}{3}})

simplify ln(x^2)-ln(y^2)simplify

ln (x^{2}) - ln (y^{2})

expand log_{2}((3^6*7)^6)expand

lo g_{2} ((3^{6} \cdot 7)^{6})

Frequently Asked Questions (FAQ)

What is 12+4ln(9/5) ?
The solution to 12+4ln(9/5) is 12+4(2ln(3)-ln(5))