What is 3/2 ln(4x^6)-4/5 ln(2y^{10}) ?

The solution to 3/2 ln(4x^6)-4/5 ln(2y^{10}) is ln((4\sqrt[5]{2}x^9)/(y^8))

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simplify 3/2 ln(4x^6)-4/5 ln(2y^{10})

simplify

\frac{3}{2} ln (4 x^{6}) - \frac{4}{5} ln (2 y^{10})

Solution steps

\frac{3}{2} ln (4 x^{6}) - \frac{4}{5} ln (2 y^{10})

Apply log rule:

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

\frac{3}{2} ln (4 x^{6}) = ln ((4 x^{6})^{\frac{3}{2}})

= ln ((4 x^{6})^{\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 ((4 x^{6})^{\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 ((4 x^{6})^{\frac{3}{2}}) - ln ((2 y^{10})^{\frac{4}{5}}) = ln \frac{( 4 x ^{6} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

= ln \frac{( 4 x ^{6} ) ^{\frac{3}{2}}}{( 2 y ^{10} ) ^{\frac{4}{5}}}

Simplify

0.5 ln (\frac{10.5}{6.5})

- \frac{1}{1.2097 \cdot 1 0 ^{- 4}} ln (\frac{20}{22})

- ln ∣ 5.1 - 3 ∣ + 2 ln ∣ 5.1 - 2 ∣

2 ln (x) + 3 ln (1 + x) - 4 ln (2 + x)

ln (\frac{463.15}{343.15})

What is 3/2 ln(4x^6)-4/5 ln(2y^{10}) ?
The solution to 3/2 ln(4x^6)-4/5 ln(2y^{10}) is ln((4\sqrt[5]{2}x^9)/(y^8))