What is log_{10}((sqrt(x^3))/(2x+4)) ?

The solution to log_{10}((sqrt(x^3))/(2x+4)) is log_{10}(x)+log_{10}(sqrt(x))-log_{10}(2x+4)

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simplify log_{10}((sqrt(x^3))/(2x+4))

simplify

lo g_{10} (\frac{x ^{3}}{2 x + 4})

lo g_{10} (x) + lo g_{10} (x) - lo g_{10} (2 x + 4)

Solution steps

lo g_{10} (\frac{x ^{3}}{2 x + 4})

Simplify

x^{3} : x x

= lo g_{10} (\frac{x x}{2 x + 4})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x x}{2 x + 4}) = lo g_{10} (x x) - lo g_{10} (2 x + 4)

= lo g_{10} (x x) - lo g_{10} (2 x + 4)

Simplify

lo g_{10} (x x) : lo g_{10} (x) + lo g_{10} (x)

= lo g_{10} (x) + lo g_{10} (x) - lo g_{10} (2 x + 4)

lo g_{5} (x) + 2 lo g_{5} (y) - \frac{1}{2} lo g_{5} (17)

lo g_{10} (a b^{x})

lo g_{10} (\frac{x ( x + 2 )}{( x + 4 ) ^{2}})

3 ln (\frac{5}{3})

ln (6) + ln (x)

What is log_{10}((sqrt(x^3))/(2x+4)) ?
The solution to log_{10}((sqrt(x^3))/(2x+4)) is log_{10}(x)+log_{10}(sqrt(x))-log_{10}(2x+4)