What is ln(9)-3ln(x)-2ln(y) ?

The solution to ln(9)-3ln(x)-2ln(y) is ln(9/(x^3y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(9)-3ln(x)-2ln(y)

simplify

ln (9) - 3 ln (x) - 2 ln (y)

ln (\frac{9}{x ^{3} y ^{2}})

Solution steps

ln (9) - 3 ln (x) - 2 ln (y)

Apply log rule:

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

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

= ln (9) - ln (x^{3}) - 2 ln (y)

Apply log rule:

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

ln (9) - ln (x^{3}) = ln (\frac{9}{x ^{3}})

= ln (\frac{9}{x ^{3}}) - 2 ln (y)

Apply log rule:

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

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

= ln (\frac{9}{x ^{3}}) - ln (y^{2})

Apply log rule:

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

ln (\frac{9}{x ^{3}}) - ln (y^{2}) = ln (\frac{\frac{9}{x ^{3}}}{y ^{2}})

= ln (\frac{\frac{9}{x ^{3}}}{y ^{2}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{9}{x ^{3} y ^{2}})

lo g_{10} (2) + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (\frac{4.1 \cdot 1 0 ^{8}}{1.7 \cdot 1 0 ^{7}})

3 ln (\frac{11}{10.5})

2 lo g_{c} (m) - lo g_{c} (n)

5 ln (\frac{9}{8})

What is ln(9)-3ln(x)-2ln(y) ?
The solution to ln(9)-3ln(x)-2ln(y) is ln(9/(x^3y^2))