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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{1 0 ^{- 4} x ^{- 2}}{x ^{5}})

- \frac{2}{5} lo g_{2} (\frac{2}{5}) - \frac{3}{5} lo g_{2} (\frac{3}{5})

lo g_{10} (\frac{x}{10})

- \frac{3}{5} lo g_{2} (\frac{3}{5}) - \frac{2}{5} lo g_{2} (\frac{2}{5})

lo g_{3} (27 x)

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