What is log_{10}(x^{1/2})+log_{10}((x+1)^3) ?

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

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simplify log_{10}(x^{1/2})+log_{10}((x+1)^3)

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

lo g_{2} (12) + lo g_{2} (3) - 2 lo g_{2} (2)

lo g_{10} (10 x^{5})

lo g_{5} (25 z)

- \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + C

ln (\frac{( 2 x + 1 ) ^{\frac{1}{3}}}{( 3 x - 2 ) ^{\frac{1}{4}}})

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