en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4ln(y)-3ln(x)

Solution

simplify

4 ln (y) - 3 ln (x)

Solution

ln (\frac{y ^{4}}{x ^{3}})

Solution steps

4 ln (y) - 3 ln (x)

Apply log rule:

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

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

= ln (y^{4}) - 3 ln (x)

Apply log rule:

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

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

= ln (y^{4}) - ln (x^{3})

Apply log rule:

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

ln (y^{4}) - ln (x^{3}) = ln (\frac{y ^{4}}{x ^{3}})

= ln (\frac{y ^{4}}{x ^{3}})

Popular Examples

expand ln((1+i)^5)expand

ln ((1 + i)^{5})

simplify ln(x/(x-1))simplify

ln (\frac{x}{x - 1})

simplify ln(5)-2ln(6)-ln(25)simplify

ln (5) - 2 ln (6) - ln (25)

simplify ln(2*5^2)simplify

ln (2 \cdot 5^{2})

simplify ln(2e)-1 simplify

ln (2 e) - 1

Frequently Asked Questions (FAQ)

What is 4ln(y)-3ln(x) ?
The solution to 4ln(y)-3ln(x) is ln((y^4)/(x^3))