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

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

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

expand

lo g_{10} (10000 t)

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

Solution steps

lo g_{10} (10000 t)

10000 t = 100 t

= lo g_{10} (100 t)

Apply log rule:

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

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

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

Simplify

lo g_{10} (100) : 2

Rewrite as

= lo g_{10} (t^{\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} (t) + 2

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