What is 2log_{2}(x)+1/2 log_{2}(y)-5log_{2}(z) ?

The solution to 2log_{2}(x)+1/2 log_{2}(y)-5log_{2}(z) is log_{2}((x^2y^{1/2})/(z^5))

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simplify 2log_{2}(x)+1/2 log_{2}(y)-5log_{2}(z)

simplify

2 lo g_{2} (x) + \frac{1}{2} lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{2} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{5}})

Solution steps

2 lo g_{2} (x) + \frac{1}{2} lo g_{2} (y) - 5 lo g_{2} (z)

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}) + \frac{1}{2} lo g_{2} (y) - 5 lo g_{2} (z)

Apply log rule:

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

\frac{1}{2} lo g_{2} (y) = lo g_{2} (y^{\frac{1}{2}})

= lo g_{2} (x^{2}) + lo g_{2} (y^{\frac{1}{2}}) - 5 lo g_{2} (z)

Apply log rule:

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

lo g_{2} (x^{2}) + lo g_{2} (y^{\frac{1}{2}}) = lo g_{2} (x^{2} y^{\frac{1}{2}})

= lo g_{2} (x^{2} y^{\frac{1}{2}}) - 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^{2} y^{\frac{1}{2}}) - 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^{2} y^{\frac{1}{2}}) - lo g_{2} (z^{5}) = lo g_{2} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{5}})

= lo g_{2} (\frac{x ^{2} y ^{\frac{1}{2}}}{z ^{5}})

lo g_{10} (\frac{11 a}{4})

lo g_{x} (\frac{1}{2})

ln (9 x) - ln (9)

What is 2log_{2}(x)+1/2 log_{2}(y)-5log_{2}(z) ?
The solution to 2log_{2}(x)+1/2 log_{2}(y)-5log_{2}(z) is log_{2}((x^2y^{1/2})/(z^5))