What is 3log_{2}(x)-log_{2}(y) ?

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

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simplify 3log_{2}(x)-log_{2}(y)

simplify

3 lo g_{2} (x) - lo g_{2} (y)

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

Solution steps

3 lo g_{2} (x) - lo g_{2} (y)

Apply log rule:

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

3 lo g_{2} (x) = lo g_{2} (x^{3})

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

Apply log rule:

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

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

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

- lo g_{10} (5.16 \cdot 1 0^{- 6})

- ln (x^{6}) - ln (y^{6})

- ln (5.8) + 2 ln (6.8) + c

\frac{1}{3} [5 ln (x + 6) + ln (x) - ln (x^{2} - 6)]

ln (\frac{ln ( e x )}{d})

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