What is expand log_{4}(sqrt(10x)) ?

The solution to expand log_{4}(sqrt(10x)) is 1/2 log_{4}(10x)

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expand log_{4}(sqrt(10x))

expand

lo g_{4} (10 x)

\frac{1}{2} lo g_{4} (10 x)

Solution steps

lo g_{4} (10 x)

Rewrite as

= lo g_{4} ((10 x)^{\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} (10 x)

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What is expand log_{4}(sqrt(10x)) ?
The solution to expand log_{4}(sqrt(10x)) is 1/2 log_{4}(10x)