What is 3log_{b}(x)-log_{b}(2)-log_{b}(x+2) ?

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

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simplify 3log_{b}(x)-log_{b}(2)-log_{b}(x+2)

simplify

3 lo g_{b} (x) - lo g_{b} (2) - lo g_{b} (x + 2)

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

Solution steps

3 lo g_{b} (x) - lo g_{b} (2) - lo g_{b} (x + 2)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{b} (x^{3}) - lo g_{b} (2) - lo g_{b} (x + 2)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

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

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

lo g_{10} (\frac{x ^{4}}{y ^{3}})

\frac{1}{3} ln ∣ 3 y + 1 ∣ + C - \frac{1}{4} ln ∣ 4 x - 3 ∣ + C

\frac{1}{2} lo g_{c} (x) + 5 lo g_{c} (y) - 3 lo g_{c} (x)

ln 2 + 3 - ln 2 + 1

lo g_{10} (\frac{x ^{2}}{z})

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