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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} (\frac{x y}{( z - 3 ) ^{2}})

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

lo g_{b} (\frac{x ^{3} y}{z ^{2}})

ln (y \frac{y}{1 - y})

lo g_{10} (\frac{x}{10000})

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