What is 1/2 log_{a}(5)-log_{a}(2) ?

The solution to 1/2 log_{a}(5)-log_{a}(2) is log_{a}((5^{1/2})/2)

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simplify 1/2 log_{a}(5)-log_{a}(2)

simplify

\frac{1}{2} lo g_{a} (5) - lo g_{a} (2)

lo g_{a} (\frac{5 ^{\frac{1}{2}}}{2})

Solution steps

\frac{1}{2} lo g_{a} (5) - lo g_{a} (2)

Apply log rule:

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

\frac{1}{2} lo g_{a} (5) = lo g_{a} (5^{\frac{1}{2}})

= lo g_{a} (5^{\frac{1}{2}}) - lo g_{a} (2)

Apply log rule:

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

lo g_{a} (5^{\frac{1}{2}}) - lo g_{a} (2) = lo g_{a} (\frac{5 ^{\frac{1}{2}}}{2})

= lo g_{a} (\frac{5 ^{\frac{1}{2}}}{2})

4 ln (\frac{4}{10})

\frac{- ln ( 2 ) - 5 ln ( x ) - 5}{x}

\frac{1}{4} ln (\frac{7}{2})

2 lo g_{10} (x) + lo g_{10} (5 x - 8)

ln (\frac{cos ( x ^{2} )}{x})

What is 1/2 log_{a}(5)-log_{a}(2) ?
The solution to 1/2 log_{a}(5)-log_{a}(2) is log_{a}((5^{1/2})/2)