What is 4log_{2}(y-3)-6log_{2}(y+9) ?

The solution to 4log_{2}(y-3)-6log_{2}(y+9) is log_{2}(((y-3)^4)/((y+9)^6))

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simplify 4log_{2}(y-3)-6log_{2}(y+9)

simplify

4 lo g_{2} (y - 3) - 6 lo g_{2} (y + 9)

lo g_{2} (\frac{( y - 3 ) ^{4}}{( y + 9 ) ^{6}})

Solution steps

4 lo g_{2} (y - 3) - 6 lo g_{2} (y + 9)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{2} (y - 3) = lo g_{2} ((y - 3)^{4})

= lo g_{2} ((y - 3)^{4}) - 6 lo g_{2} (y + 9)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 lo g_{2} (y + 9) = lo g_{2} ((y + 9)^{6})

= lo g_{2} ((y - 3)^{4}) - lo g_{2} ((y + 9)^{6})

Apply log rule:

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

lo g_{2} ((y - 3)^{4}) - lo g_{2} ((y + 9)^{6}) = lo g_{2} (\frac{( y - 3 ) ^{4}}{( y + 9 ) ^{6}})

= lo g_{2} (\frac{( y - 3 ) ^{4}}{( y + 9 ) ^{6}})

ln (- \frac{2}{5} e^{10 t})

lo g_{e} (x^{2}) - lo g_{e} (lo g_{e} (x))

ln (\frac{e ^{x^{2}}}{x ^{2}})

- lo g_{10} (x) + \frac{1}{2} lo g_{10} (y) + 1

ln (\frac{5 g ^{- 1}}{w})

What is 4log_{2}(y-3)-6log_{2}(y+9) ?
The solution to 4log_{2}(y-3)-6log_{2}(y+9) is log_{2}(((y-3)^4)/((y+9)^6))