en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln(a)-2ln(b)

Solution

simplify

4 ln (a) - 2 ln (b)

Solution

ln (\frac{a ^{4}}{b ^{2}})

Solution steps

4 ln (a) - 2 ln (b)

Apply log rule:

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

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

= ln (a^{4}) - 2 ln (b)

Apply log rule:

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

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

= ln (a^{4}) - ln (b^{2})

Apply log rule:

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

ln (a^{4}) - ln (b^{2}) = ln (\frac{a ^{4}}{b ^{2}})

= ln (\frac{a ^{4}}{b ^{2}})

Popular Examples

simplify ln(20)-ln(4)simplify

ln (20) - ln (4)

expand log_{5}((25x)^2)expand

lo g_{5} ((25 x)^{2})

simplify ln(4x^2y)simplify

ln (4 x^{2} y)

simplify log_{10}(x)+1/6 log_{10}(y)simplify

lo g_{10} (x) + \frac{1}{6} lo g_{10} (y)

simplify-0.2log_{2}(0.2)-0.8log_{2}(0.8)simplify

- 0.2 lo g_{2} (0.2) - 0.8 lo g_{2} (0.8)

Frequently Asked Questions (FAQ)

What is 4ln(a)-2ln(b) ?
The solution to 4ln(a)-2ln(b) is ln((a^4)/(b^2))