What is 6log_{5}(u)+8log_{5}(v) ?

The solution to 6log_{5}(u)+8log_{5}(v) is log_{5}(u^6v^8)

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simplify 6log_{5}(u)+8log_{5}(v)

simplify

6 lo g_{5} (u) + 8 lo g_{5} (v)

lo g_{5} (u^{6} v^{8})

Solution steps

6 lo g_{5} (u) + 8 lo g_{5} (v)

Apply log rule:

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

6 lo g_{5} (u) = lo g_{5} (u^{6})

= lo g_{5} (u^{6}) + 8 lo g_{5} (v)

Apply log rule:

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

8 lo g_{5} (v) = lo g_{5} (v^{8})

= lo g_{5} (u^{6}) + lo g_{5} (v^{8})

Apply log rule:

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

lo g_{5} (u^{6}) + lo g_{5} (v^{8}) = lo g_{5} (u^{6} v^{8})

= lo g_{5} (u^{6} v^{8})

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What is 6log_{5}(u)+8log_{5}(v) ?
The solution to 6log_{5}(u)+8log_{5}(v) is log_{5}(u^6v^8)