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

The solution to 3log_{2}(3)+log_{2}(e) is log_{2}(27e)

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

simplify

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

lo g_{2} (27 e)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{3} = 27

= lo g_{2} (27 e)

ln (2 x) - x^{2} + 5

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

ln (\frac{1}{2}) \cdot 2

ln (5) + ln (20)

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

What is 3log_{2}(3)+log_{2}(e) ?
The solution to 3log_{2}(3)+log_{2}(e) is log_{2}(27e)