What is 4log_{b}(x+2)-1/3 log_{b}(x-5) ?

The solution to 4log_{b}(x+2)-1/3 log_{b}(x-5) is log_{b}(((x+2)^4(x-5)^{2/3})/(x-5))

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simplify 4log_{b}(x+2)-1/3 log_{b}(x-5)

simplify

4 lo g_{b} (x + 2) - \frac{1}{3} lo g_{b} (x - 5)

lo g_{b} (\frac{( x + 2 ) ^{4} ( x - 5 ) ^{\frac{2}{3}}}{x - 5})

Solution steps

4 lo g_{b} (x + 2) - \frac{1}{3} lo g_{b} (x - 5)

Apply log rule:

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

4 lo g_{b} (x + 2) = lo g_{b} ((x + 2)^{4})

= lo g_{b} ((x + 2)^{4}) - \frac{1}{3} lo g_{b} (x - 5)

Apply log rule:

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

\frac{1}{3} lo g_{b} (x - 5) = lo g_{b} ((x - 5)^{\frac{1}{3}})

= lo g_{b} ((x + 2)^{4}) - lo g_{b} ((x - 5)^{\frac{1}{3}})

Apply log rule:

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

lo g_{b} ((x + 2)^{4}) - lo g_{b} ((x - 5)^{\frac{1}{3}}) = lo g_{b} (\frac{( x + 2 ) ^{4}}{( x - 5 ) ^{\frac{1}{3}}})

= lo g_{b} (\frac{( x + 2 ) ^{4}}{( x - 5 ) ^{\frac{1}{3}}})

Simplify

\frac{( x + 2 ) ^{4}}{( x - 5 ) ^{\frac{1}{3}}} : \frac{( x + 2 ) ^{4} ( x - 5 ) ^{\frac{2}{3}}}{x - 5}

= lo g_{b} (\frac{( x + 2 ) ^{4} ( x - 5 ) ^{\frac{2}{3}}}{x - 5})

ln (\frac{4 m ^{5}}{p})

ln (\frac{x ^{3}}{y ^{2}})

lo g_{5} (x^{2}) - 3 lo g_{5} (x)

2 lo g_{10} (3) + 3 lo g_{10} (2)

y (ln (x) - ln (y))

What is 4log_{b}(x+2)-1/3 log_{b}(x-5) ?
The solution to 4log_{b}(x+2)-1/3 log_{b}(x-5) is log_{b}(((x+2)^4(x-5)^{2/3})/(x-5))