What is log_{a}((x-x^{1/2})/((x-y)^3)) ?

The solution to log_{a}((x-x^{1/2})/((x-y)^3)) is log_{a}(x-x^{1/2})-3log_{a}(x-y)

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simplify log_{a}((x-x^{1/2})/((x-y)^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{a} ((x - y)^{3}) = 3 lo g_{a} (x - y)

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

lo g_{2} (\frac{2 ( 3 x + 4 ) ^{2}}{2 ^{5} ( x + 1 ) ^{2}})

f (x) = ln (x) - \frac{1}{2} \cdot ln (x^{2} + 1)

ln (1.14 \cdot 86262850832)

ln (\frac{x ^{5} y ^{7}}{z w ^{4}})

What is log_{a}((x-x^{1/2})/((x-y)^3)) ?
The solution to log_{a}((x-x^{1/2})/((x-y)^3)) is log_{a}(x-x^{1/2})-3log_{a}(x-y)