What is 4log_{2}(x)-5log_{2}(y) ?

The solution to 4log_{2}(x)-5log_{2}(y) is log_{2}((x^4)/(y^5))

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simplify 4log_{2}(x)-5log_{2}(y)

simplify

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

lo g_{2} (\frac{x ^{4}}{y ^{5}})

Solution steps

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

Apply log rule:

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

4 lo g_{2} (x) = lo g_{2} (x^{4})

= lo g_{2} (x^{4}) - 5 lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (x^{4}) - lo g_{2} (y^{5})

Apply log rule:

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

lo g_{2} (x^{4}) - lo g_{2} (y^{5}) = lo g_{2} (\frac{x ^{4}}{y ^{5}})

= lo g_{2} (\frac{x ^{4}}{y ^{5}})

lo g_{b} (\frac{a ^{3} c ^{4}}{a})

lo g_{5} (x) + lo g_{5} (10) + lo g_{5} (y)

ln (a) + 2 ln (a + b) - 4 ln (ab)

lo g_{9} (4) + lo g_{9} (5)

lo g_{3} (y) + lo g_{3} (y + 4)

What is 4log_{2}(x)-5log_{2}(y) ?
The solution to 4log_{2}(x)-5log_{2}(y) is log_{2}((x^4)/(y^5))