What is expand ln(((y-1)/4)^2) ?

The solution to expand ln(((y-1)/4)^2) is 2(ln(y-1)-2ln(2))

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expand ln(((y-1)/4)^2)

expand

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

2 (ln (y - 1) - 2 ln (2))

Solution steps

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

Apply log rule:

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

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

= 2 ln (\frac{y - 1}{4})

Apply log rule:

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

ln (\frac{y - 1}{4}) = ln (y - 1) - ln (4)

= 2 (ln (y - 1) - ln (4))

ln (4) = 2 ln (2)

= 2 (ln (y - 1) - 2 ln (2))

ln (\frac{120}{100})

lo g_{7} (35) + lo g_{7} (5)

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

lo g_{5} (8) + lo g_{5} (11)

2 lo g_{10} (m) + 3 lo g_{10} (n) - 4 lo g_{10} (y)

What is expand ln(((y-1)/4)^2) ?
The solution to expand ln(((y-1)/4)^2) is 2(ln(y-1)-2ln(2))