What is expand log_{10}(sqrt(x^2(x+2))) ?

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

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expand log_{10}(sqrt(x^2(x+2)))

expand

lo g_{10} (x^{2} (x + 2))

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

Solution steps

lo g_{10} (x^{2} (x + 2))

x^{2} (x + 2) = x x + 2

= lo g_{10} (x x + 2)

Apply log rule:

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

lo g_{10} (x x + 2) = lo g_{10} (x) + lo g_{10} (x + 2)

= lo g_{10} (x) + lo g_{10} (x + 2)

Simplify

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

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

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\frac{3 ( a + b ) ^{2}}{2}

(7 x^{\frac{5}{3}} + 49 x^{\frac{2}{3}}) (5)

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