What is 4log_{10}(x)-1/3 log_{10}(x+6) ?

The solution to 4log_{10}(x)-1/3 log_{10}(x+6) is log_{10}((x^4(x+6)^{2/3})/(x+6))

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simplify 4log_{10}(x)-1/3 log_{10}(x+6)

simplify

4 lo g_{10} (x) - \frac{1}{3} lo g_{10} (x + 6)

lo g_{10} (\frac{x ^{4} ( x + 6 ) ^{\frac{2}{3}}}{x + 6})

Solution steps

4 lo g_{10} (x) - \frac{1}{3} lo g_{10} (x + 6)

Apply log rule:

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

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

= lo g_{10} (x^{4}) - \frac{1}{3} lo g_{10} (x + 6)

Apply log rule:

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

\frac{1}{3} lo g_{10} (x + 6) = lo g_{10} ((x + 6)^{\frac{1}{3}})

= lo g_{10} (x^{4}) - lo g_{10} ((x + 6)^{\frac{1}{3}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{4}) - lo g_{10} ((x + 6)^{\frac{1}{3}}) = lo g_{10} (\frac{x ^{4}}{( x + 6 ) ^{\frac{1}{3}}})

= lo g_{10} (\frac{x ^{4}}{( x + 6 ) ^{\frac{1}{3}}})

Simplify

\frac{x ^{4}}{( x + 6 ) ^{\frac{1}{3}}} : \frac{x ^{4} ( x + 6 ) ^{\frac{2}{3}}}{x + 6}

= lo g_{10} (\frac{x ^{4} ( x + 6 ) ^{\frac{2}{3}}}{x + 6})

9 ln (\frac{9}{2})

4 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (w)

lo g_{10} (\frac{4 ^{7} - 9 ^{4}}{6 ^{5}})

ln (\frac{e ^{2 x}}{x})

ln (\frac{2000}{1999})

What is 4log_{10}(x)-1/3 log_{10}(x+6) ?
The solution to 4log_{10}(x)-1/3 log_{10}(x+6) is log_{10}((x^4(x+6)^{2/3})/(x+6))