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

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

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simplify 3log_{2}(a)+2log_{2}(b)

simplify

3 lo g_{2} (a) + 2 lo g_{2} (b)

lo g_{2} (a^{3} b^{2})

Solution steps

3 lo g_{2} (a) + 2 lo g_{2} (b)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (y) - ln (y - 3)

10 lo g_{10} (\frac{i}{1 0 ^{12} i _{0}})

ln (\frac{2}{80})

600 ln (600) + 400 ln (400)

ln (\frac{sin ( y )}{cos ( x )})

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