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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

lo g_{4} (13 b^{6} c)

lo g_{5} (\frac{25}{x + 2})

lo g_{4} (16 x^{4}) - lo g_{4} ((2 x)^{2})

- lo g_{10} (7.2 \cdot 1 0^{- 7})

3 ln (2) + \frac{1}{3} ln (8) - \frac{1}{2} ln (25)

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