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

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

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

simplify

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

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

Solution steps

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

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

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

lo g_{2} (32 x^{3})

lo g_{10} (2 x)

\frac{1}{3} [ln (x) + 2 ln (x + 4)] - ln (x - 1)

4 [ln (z) + ln (z + 7)] - 2 ln (z - 7)

ln (x^{2}) - 2 ln (x)

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