What is expand ln((((x+3)^3)/(4x))^{-2}) ?

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

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expand ln((((x+3)^3)/(4x))^{-2})

expand

ln (\frac{( x + 3 ) ^{3}}{4 x})^{- 2}

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

Solution steps

ln (\frac{( x + 3 ) ^{3}}{4 x})^{- 2}

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{( x + 3 ) ^{3}}{4 x}) = ln ((x + 3)^{3}) - ln (4 x)

= - 2 (ln ((x + 3)^{3}) - ln (4 x))

Apply log rule:

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

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

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

- lo g_{10} (1.509645 \cdot 1 0^{- 3})

lo g_{10} (u v^{4} \cdot w^{4})

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

9 lo g_{10} (x) - 4 lo g_{10} (y)

ln (\frac{7 x}{x - 7})

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