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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{1}{k})

ln (13) - ln (3)

\frac{1}{10} ln (\frac{550}{500})

- ln (\frac{1}{2}) + ln (1)

ln (10) - ln (7)

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