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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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