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

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

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

simplify

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

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

Solution steps

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

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

ln (\frac{\frac{108}{180}}{- 5})

\frac{1}{3} ln (\frac{11}{7})

\frac{1}{2} ln (36) + 2 ln (4) - ln (4)

lo g_{10} (z^{4} x)

ln (0.7) - ln (0.3)

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