What is 2log_{2}(y-6)-4log_{2}(y+7) ?

The solution to 2log_{2}(y-6)-4log_{2}(y+7) is log_{2}(((y-6)^2)/((y+7)^4))

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simplify 2log_{2}(y-6)-4log_{2}(y+7)

simplify

2 lo g_{2} (y - 6) - 4 lo g_{2} (y + 7)

lo g_{2} (\frac{( y - 6 ) ^{2}}{( y + 7 ) ^{4}})

Solution steps

2 lo g_{2} (y - 6) - 4 lo g_{2} (y + 7)

Apply log rule:

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

2 lo g_{2} (y - 6) = lo g_{2} ((y - 6)^{2})

= lo g_{2} ((y - 6)^{2}) - 4 lo g_{2} (y + 7)

Apply log rule:

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

4 lo g_{2} (y + 7) = lo g_{2} ((y + 7)^{4})

= lo g_{2} ((y - 6)^{2}) - lo g_{2} ((y + 7)^{4})

Apply log rule:

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

lo g_{2} ((y - 6)^{2}) - lo g_{2} ((y + 7)^{4}) = lo g_{2} (\frac{( y - 6 ) ^{2}}{( y + 7 ) ^{4}})

= lo g_{2} (\frac{( y - 6 ) ^{2}}{( y + 7 ) ^{4}})

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What is 2log_{2}(y-6)-4log_{2}(y+7) ?
The solution to 2log_{2}(y-6)-4log_{2}(y+7) is log_{2}(((y-6)^2)/((y+7)^4))