What is expand log_{e}(((y-1)/3)^2) ?

The solution to expand log_{e}(((y-1)/3)^2) is 2(ln(y-1)-ln(3))

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expand log_{e}(((y-1)/3)^2)

expand

lo g_{e} ((\frac{y - 1}{3})^{2})

2 (ln (y - 1) - ln (3))

Solution steps

lo g_{e} ((\frac{y - 1}{3})^{2})

Apply log rule:

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

lo g_{e} ((\frac{y - 1}{3})^{2}) = 2 lo g_{e} (\frac{y - 1}{3})

= 2 lo g_{e} (\frac{y - 1}{3})

Apply log rule:

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

lo g_{e} (\frac{y - 1}{3}) = lo g_{e} (y - 1) - lo g_{e} (3)

= 2 (lo g_{e} (y - 1) - lo g_{e} (3))

Apply log rule:

lo g_{e} (x) = ln (x)

= 2 (ln (y - 1) - lo g_{e} (3))

Apply log rule:

lo g_{e} (x) = ln (x)

= 2 (ln (y - 1) - ln (3))

16 + 4 ln (\frac{5}{3})

15 + 10 ln (x) - 15 ln (y)

ln (\frac{30}{5})

so l v e (0 = \frac{1}{2} (2) - \frac{1}{2} ln (2^{\frac{1}{2}}) + c, c)

lo g_{10} (\frac{y ^{5}}{z ^{2} x})

What is expand log_{e}(((y-1)/3)^2) ?
The solution to expand log_{e}(((y-1)/3)^2) is 2(ln(y-1)-ln(3))