What is expand log_{4}(sqrt(ab)) ?

The solution to expand log_{4}(sqrt(ab)) is 1/2 log_{4}(ab)

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expand log_{4}(sqrt(ab))

expand

lo g_{4} (ab)

\frac{1}{2} lo g_{4} (ab)

Solution steps

lo g_{4} (ab)

Rewrite as

= lo g_{4} ((ab)^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} lo g_{4} (ab)

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What is expand log_{4}(sqrt(ab)) ?
The solution to expand log_{4}(sqrt(ab)) is 1/2 log_{4}(ab)