What is 1/3 log_{6}(x)+2log_{6}(x+1)+3 ?

The solution to 1/3 log_{6}(x)+2log_{6}(x+1)+3 is log_{6}(x^{1/3}(x+1)^2)+3

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simplify 1/3 log_{6}(x)+2log_{6}(x+1)+3

simplify

\frac{1}{3} lo g_{6} (x) + 2 lo g_{6} (x + 1) + 3

lo g_{6} (x^{\frac{1}{3}} (x + 1)^{2}) + 3

Solution steps

\frac{1}{3} lo g_{6} (x) + 2 lo g_{6} (x + 1) + 3

Apply log rule:

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

\frac{1}{3} lo g_{6} (x) = lo g_{6} (x^{\frac{1}{3}})

= lo g_{6} (x^{\frac{1}{3}}) + 2 lo g_{6} (x + 1) + 3

Apply log rule:

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

2 lo g_{6} (x + 1) = lo g_{6} ((x + 1)^{2})

= lo g_{6} (x^{\frac{1}{3}}) + lo g_{6} ((x + 1)^{2}) + 3

Apply log rule:

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

lo g_{6} (x^{\frac{1}{3}}) + lo g_{6} ((x + 1)^{2}) = lo g_{6} (x^{\frac{1}{3}} (x + 1)^{2})

= lo g_{6} (x^{\frac{1}{3}} (x + 1)^{2}) + 3

(\frac{17}{12})^{2} ln (\frac{17}{12})

lo g_{4} (\frac{e ^{x} + 9}{- 4})

ln (\frac{8192}{625})

12.75 + lo g_{10} (\frac{0.05}{0.15})

lo g_{\frac{1}{2}} (\frac{1}{50})

What is 1/3 log_{6}(x)+2log_{6}(x+1)+3 ?
The solution to 1/3 log_{6}(x)+2log_{6}(x+1)+3 is log_{6}(x^{1/3}(x+1)^2)+3