What is 6log_{b}(m)-5log_{b}(n)+3 ?

The solution to 6log_{b}(m)-5log_{b}(n)+3 is log_{b}((m^6)/(n^5))+3

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simplify 6log_{b}(m)-5log_{b}(n)+3

simplify

6 lo g_{b} (m) - 5 lo g_{b} (n) + 3

lo g_{b} (\frac{m ^{6}}{n ^{5}}) + 3

Solution steps

6 lo g_{b} (m) - 5 lo g_{b} (n) + 3

Apply log rule:

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

6 lo g_{b} (m) = lo g_{b} (m^{6})

= lo g_{b} (m^{6}) - 5 lo g_{b} (n) + 3

Apply log rule:

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

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

= lo g_{b} (m^{6}) - lo g_{b} (n^{5}) + 3

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{b} (m^{6}) - lo g_{b} (n^{5}) = lo g_{b} (\frac{m ^{6}}{n ^{5}})

= lo g_{b} (\frac{m ^{6}}{n ^{5}}) + 3

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What is 6log_{b}(m)-5log_{b}(n)+3 ?
The solution to 6log_{b}(m)-5log_{b}(n)+3 is log_{b}((m^6)/(n^5))+3