What is log_{2}(a)+1/2 log_{2}(b)-3log_{2}(c) ?

The solution to log_{2}(a)+1/2 log_{2}(b)-3log_{2}(c) is log_{2}((ab^{1/2})/(c^3))

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simplify log_{2}(a)+1/2 log_{2}(b)-3log_{2}(c)

simplify

lo g_{2} (a) + \frac{1}{2} lo g_{2} (b) - 3 lo g_{2} (c)

lo g_{2} (\frac{a b ^{\frac{1}{2}}}{c ^{3}})

Solution steps

lo g_{2} (a) + \frac{1}{2} lo g_{2} (b) - 3 lo g_{2} (c)

Apply log rule:

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

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

= lo g_{2} (a) + lo g_{2} (b^{\frac{1}{2}}) - 3 lo g_{2} (c)

Apply log rule:

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

lo g_{2} (a) + lo g_{2} (b^{\frac{1}{2}}) = lo g_{2} (a b^{\frac{1}{2}})

= lo g_{2} (a b^{\frac{1}{2}}) - 3 lo g_{2} (c)

Apply log rule:

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

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

= lo g_{2} (a b^{\frac{1}{2}}) - lo g_{2} (c^{3})

Apply log rule:

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

lo g_{2} (a b^{\frac{1}{2}}) - lo g_{2} (c^{3}) = lo g_{2} (\frac{a b ^{\frac{1}{2}}}{c ^{3}})

= lo g_{2} (\frac{a b ^{\frac{1}{2}}}{c ^{3}})

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What is log_{2}(a)+1/2 log_{2}(b)-3log_{2}(c) ?
The solution to log_{2}(a)+1/2 log_{2}(b)-3log_{2}(c) is log_{2}((ab^{1/2})/(c^3))