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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

4 lo g_{3} (x) = lo g_{3} (x^{4})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (z)

lo g_{6} (\frac{16 x ^{2}}{2 x - 4})

3 lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (4 x)

lo g_{10} (5 x + 7) - lo g_{10} (x)

ln (9) - ln (2)

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