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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

\frac{1}{3} ln (4) - \frac{1}{3} ln (7)

lo g_{3} (8) + lo g_{3} (7)

lo g_{3} (8) + lo g_{3} (5)

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

ln (x e^{- 7 x})

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