What is 3/2 ln(x^{10})-4/5 ln(2y^{10}) ?

The solution to 3/2 ln(x^{10})-4/5 ln(2y^{10}) is ln((\sqrt[5]{2}x^{15})/(2y^8))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3/2 ln(x^{10})-4/5 ln(2y^{10})

simplify

\frac{3}{2} ln (x^{10}) - \frac{4}{5} ln (2 y^{10})

Solution steps

\frac{3}{2} ln (x^{10}) - \frac{4}{5} ln (2 y^{10})

Apply log rule:

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

\frac{3}{2} ln (x^{10}) = ln ((x^{10})^{\frac{3}{2}})

= ln ((x^{10})^{\frac{3}{2}}) - \frac{4}{5} ln (2 y^{10})

Apply log rule:

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

\frac{4}{5} ln (2 y^{10}) = ln ((2 y^{10})^{\frac{4}{5}})

= ln ((x^{10})^{\frac{3}{2}}) - ln ((2 y^{10})^{\frac{4}{5}})

Apply log rule:

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

ln ((x^{10})^{\frac{3}{2}}) - ln ((2 y^{10})^{\frac{4}{5}}) = ln \frac{( x ^{10} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

= ln \frac{( x ^{10} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

Simplify

- lo g_{10} (4.3 \cdot 1 0^{- 11})

ln (\frac{1 n}{1})

ln (5 \cdot 1 0^{- 4})

- lo g_{10} (7.56 \cdot 1 0^{6})

ln (373 e^{- x + 9} e^{2 y + 14})

What is 3/2 ln(x^{10})-4/5 ln(2y^{10}) ?
The solution to 3/2 ln(x^{10})-4/5 ln(2y^{10}) is ln((\sqrt[5]{2}x^{15})/(2y^8))