What is 3ln(x)-1/9 ln(z)+2ln(y) ?

The solution to 3ln(x)-1/9 ln(z)+2ln(y) is ln((x^3y^2z^{8/9})/z)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(x)-1/9 ln(z)+2ln(y)

simplify

3 ln (x) - \frac{1}{9} ln (z) + 2 ln (y)

ln (\frac{x ^{3} y ^{2} z ^{\frac{8}{9}}}{z})

Solution steps

3 ln (x) - \frac{1}{9} ln (z) + 2 ln (y)

Apply log rule:

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

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

= ln (x^{3}) - \frac{1}{9} ln (z) + 2 ln (y)

Apply log rule:

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

\frac{1}{9} ln (z) = ln (z^{\frac{1}{9}})

= ln (x^{3}) - ln (z^{\frac{1}{9}}) + 2 ln (y)

Apply log rule:

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

ln (x^{3}) - ln (z^{\frac{1}{9}}) = ln (\frac{x ^{3}}{z ^{\frac{1}{9}}})

= ln (\frac{x ^{3}}{z ^{\frac{1}{9}}}) + 2 ln (y)

Simplify

\frac{x ^{3}}{z ^{\frac{1}{9}}} : \frac{x ^{3} z ^{\frac{8}{9}}}{z}

= ln (\frac{x ^{3} z ^{\frac{8}{9}}}{z}) + 2 ln (y)

Apply log rule:

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

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

= ln (\frac{x ^{3} z ^{\frac{8}{9}}}{z}) + ln (y^{2})

Apply log rule:

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

ln (\frac{x ^{3} z ^{\frac{8}{9}}}{z}) + ln (y^{2}) = ln (\frac{x ^{3} z ^{\frac{8}{9}}}{z} y^{2})

= ln (\frac{x ^{3} z ^{\frac{8}{9}}}{z} y^{2})

Simplify

\frac{x ^{3} z ^{\frac{8}{9}}}{z} y^{2} : \frac{x ^{3} y ^{2} z ^{\frac{8}{9}}}{z}

= ln (\frac{x ^{3} y ^{2} z ^{\frac{8}{9}}}{z})

ln (20.35) - ln (- 147.65)

\frac{1}{3} ln (\frac{10}{6})

ln (12) + \frac{1}{2} ln (\frac{x}{2}) + \frac{1}{2} ln ((\frac{x}{2}) R)

ln (\frac{0.01}{0.05})

What is 3ln(x)-1/9 ln(z)+2ln(y) ?
The solution to 3ln(x)-1/9 ln(z)+2ln(y) is ln((x^3y^2z^{8/9})/z)