What is expand log_{10}(sqrt(10000s)) ?

The solution to expand log_{10}(sqrt(10000s)) is 1/2 log_{10}(s)+2

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expand log_{10}(sqrt(10000s))

expand

lo g_{10} (10000 s)

\frac{1}{2} lo g_{10} (s) + 2

Solution steps

lo g_{10} (10000 s)

10000 s = 100 s

= lo g_{10} (100 s)

Apply log rule:

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

lo g_{10} (100 s) = lo g_{10} (s) + lo g_{10} (100)

= lo g_{10} (s) + lo g_{10} (100)

Simplify

lo g_{10} (100) : 2

Rewrite as

= lo g_{10} (s^{\frac{1}{2}}) + 2

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} lo g_{10} (s) + 2

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What is expand log_{10}(sqrt(10000s)) ?
The solution to expand log_{10}(sqrt(10000s)) is 1/2 log_{10}(s)+2