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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

ln^{3} (a b^{2})

ln (\frac{a + 1}{a})

ln_{3} (0.2) + ln_{3} (1215)

lo g_{10} (1215 x^{0.84})

ln (x) - 3 ln (z) + 0.5 ln (y)

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