What is 5log_{2}(x)-3log_{2}(y) ?

The solution to 5log_{2}(x)-3log_{2}(y) is log_{2}((x^5)/(y^3))

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simplify 5log_{2}(x)-3log_{2}(y)

simplify

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

lo g_{2} (\frac{x ^{5}}{y ^{3}})

Solution steps

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

Apply log rule:

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

5 lo g_{2} (x) = lo g_{2} (x^{5})

= lo g_{2} (x^{5}) - 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^{5}) - 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^{5}) - lo g_{2} (y^{3}) = lo g_{2} (\frac{x ^{5}}{y ^{3}})

= lo g_{2} (\frac{x ^{5}}{y ^{3}})

lo g_{b} (\frac{x ^{4}}{z ^{2}})

2 (ln (x) - ln (x + 1) - ln (x - 1))

2 ln (x) + 3 ln (x + 1)

ln (e (x - 8))

ln (a e^{b})

What is 5log_{2}(x)-3log_{2}(y) ?
The solution to 5log_{2}(x)-3log_{2}(y) is log_{2}((x^5)/(y^3))