What is expand ln(((10x)/(3y))^2) ?

The solution to expand ln(((10x)/(3y))^2) is 2(ln(10x)-ln(3y))

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expand ln(((10x)/(3y))^2)

expand

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

2 (ln (10 x) - ln (3 y))

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{10 x}{3 y}) = ln (10 x) - ln (3 y)

= 2 (ln (10 x) - ln (3 y))

lo g_{4} (\frac{x}{5})

- lo g_{10} (6.31 \cdot 1 0^{- 6})

3 ln (x) + ln (x^{(4)}) - ln ((x^{3}) (e^{x}))

ln (2.6 x 1 0^{- 16}) - ln (3.4 x 1 0^{- 16})

ln (\frac{x y ^{4}}{z ^{3}})

What is expand ln(((10x)/(3y))^2) ?
The solution to expand ln(((10x)/(3y))^2) is 2(ln(10x)-ln(3y))