What is log_{2}((sqrt(x+y))/((x-y)^4)) ?

The solution to log_{2}((sqrt(x+y))/((x-y)^4)) is log_{2}(sqrt(x+y))-4log_{2}(x-y)

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simplify log_{2}((sqrt(x+y))/((x-y)^4))

simplify

lo g_{2} (\frac{x + y}{( x - y ) ^{4}})

lo g_{2} (x + y) - 4 lo g_{2} (x - y)

Solution steps

lo g_{2} (\frac{x + y}{( x - y ) ^{4}})

Apply log rule:

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

lo g_{2} (\frac{x + y}{( x - y ) ^{4}}) = lo g_{2} (x + y) - lo g_{2} ((x - y)^{4})

= lo g_{2} (x + y) - lo g_{2} ((x - y)^{4})

Apply log rule:

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

lo g_{2} ((x - y)^{4}) = 4 lo g_{2} (x - y)

= lo g_{2} (x + y) - 4 lo g_{2} (x - y)

lo g_{3} (\frac{x ^{4}}{3 y ^{3}})

ln (7) - ln (4)

ln (p^{4}) + ln (3 p^{5}) - 2 ln (p)

lo g_{3} (92) + \frac{1}{2} lo g_{3} (x)

3 lo g_{3} (u) + 6 lo g_{3} (v) + lo g_{3} (w)

What is log_{2}((sqrt(x+y))/((x-y)^4)) ?
The solution to log_{2}((sqrt(x+y))/((x-y)^4)) is log_{2}(sqrt(x+y))-4log_{2}(x-y)