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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

21 lo g_{10} (x) - 5 lo g_{10} (q) + lo g_{10} (z^{2})

lo g_{10} (4) + lo g_{10} (8)

lo g_{10} (4) + lo g_{10} (5) + lo g_{10} (3)

lo g_{2} (2 x) - lo g_{2} (x + 1)

ln (\frac{e}{4})

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