What is 4log_{2}(m)+5log_{2}(n) ?

The solution to 4log_{2}(m)+5log_{2}(n) is log_{2}(m^4n^5)

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simplify 4log_{2}(m)+5log_{2}(n)

simplify

4 lo g_{2} (m) + 5 lo g_{2} (n)

lo g_{2} (m^{4} n^{5})

Solution steps

4 lo g_{2} (m) + 5 lo g_{2} (n)

Apply log rule:

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

4 lo g_{2} (m) = lo g_{2} (m^{4})

= lo g_{2} (m^{4}) + 5 lo g_{2} (n)

Apply log rule:

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

5 lo g_{2} (n) = lo g_{2} (n^{5})

= lo g_{2} (m^{4}) + lo g_{2} (n^{5})

Apply log rule:

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

lo g_{2} (m^{4}) + lo g_{2} (n^{5}) = lo g_{2} (m^{4} n^{5})

= lo g_{2} (m^{4} n^{5})

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What is 4log_{2}(m)+5log_{2}(n) ?
The solution to 4log_{2}(m)+5log_{2}(n) is log_{2}(m^4n^5)