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

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

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simplify log_{2}(x)+5log_{2}(y)-5log_{2}(z)

simplify

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

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

Solution steps

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

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) + lo g_{2} (y^{5}) - 5 lo g_{2} (z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{x ^{2}}{2})

\frac{1}{2} ln (x + 1) - \frac{1}{4} ln (x^{2} + 1)

5 lo g_{10} (a) - 25 lo g_{10} (b)

2 lo g_{m} (a) - 3 lo g_{m} (b^{2})

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