What is expand log_{10}(sqrt(7x^3)) ?

The solution to expand log_{10}(sqrt(7x^3)) is 3/2 log_{10}(x)+1/2 log_{10}(7)

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expand log_{10}(sqrt(7x^3))

expand

lo g_{10} (7 x^{3})

\frac{3}{2} lo g_{10} (x) + \frac{1}{2} lo g_{10} (7)

Solution steps

lo g_{10} (7 x^{3})

7 x^{3} = 7 x x

= lo g_{10} (7 x x)

Apply log rule:

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

lo g_{10} (7 x x) = lo g_{10} (x x) + lo g_{10} (7)

= lo g_{10} (x x) + lo g_{10} (7)

Simplify

lo g_{10} (7) : \frac{1}{2} lo g_{10} (7)

= lo g_{10} (x x) + \frac{1}{2} lo g_{10} (7)

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

= \frac{3}{2} lo g_{10} (x) + \frac{1}{2} lo g_{10} (7)

(k + 1) (k^{2} + k + 1)

\frac{- 2 x ^{2} - 2 x + 2}{( x ^{2} + 1 ) ^{2}}

3 (5 - 11)

(e^{x} sin (2 x) + 2 e^{x} cos (2 x))^{2}

162 (3 π - 4)

What is expand log_{10}(sqrt(7x^3)) ?
The solution to expand log_{10}(sqrt(7x^3)) is 3/2 log_{10}(x)+1/2 log_{10}(7)