What is expand log_{10}(sqrt(t^3)) ?

The solution to expand log_{10}(sqrt(t^3)) is 3/2 log_{10}(t)

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expand log_{10}(sqrt(t^3))

expand

lo g_{10} (t^{3})

\frac{3}{2} lo g_{10} (t)

Solution steps

lo g_{10} (t^{3})

t^{3} = t t

= lo g_{10} (t t)

Apply log rule:

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

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

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

Simplify

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

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

Factor out common term

lo g_{10} (t)

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

1 + \frac{1}{2} = \frac{3}{2}

= \frac{3}{2} lo g_{10} (t)

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What is expand log_{10}(sqrt(t^3)) ?
The solution to expand log_{10}(sqrt(t^3)) is 3/2 log_{10}(t)