What is expand ln((3d^2)/(4^{-1)}) ?

The solution to expand ln((3d^2)/(4^{-1)}) is ln(3)+2ln(d)--1*ln(4)

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expand ln((3d^2)/(4^{-1)})

expand

ln (\frac{3 d ^{2}}{4 ^{- 1}})

ln (3) + 2 ln (d) - - 1 \cdot ln (4)

Solution steps

ln (\frac{3 d ^{2}}{4 ^{- 1}})

Apply log rule:

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

ln (\frac{3 d ^{2}}{4 ^{- 1}}) = ln (3 d^{2}) - ln (4^{- 1})

= ln (3 d^{2}) - ln (4^{- 1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (4^{- 1}) = - 1 \cdot ln (4)

= ln (3 d^{2}) - - 1 \cdot ln (4)

Apply log rule:

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

ln (3 d^{2}) = ln (3) + ln (d^{2})

= ln (3) + ln (d^{2}) - - 1 \cdot ln (4)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (3) + 2 ln (d) - - 1 \cdot ln (4)

(\frac{1}{2}) ln (\frac{0.7}{0.3})

ln (2 x e^{x})

lo g_{10} (4) + lo g_{10} (7)

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

What is expand ln((3d^2)/(4^{-1)}) ?
The solution to expand ln((3d^2)/(4^{-1)}) is ln(3)+2ln(d)--1*ln(4)