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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= \frac{1}{2} lo g_{a} (3) + \frac{1}{2} lo g_{a} (lo g_{b} (x))

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