What is 3log_{6}(u)+5log_{6}(v) ?

The solution to 3log_{6}(u)+5log_{6}(v) is log_{6}(u^3v^5)

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simplify 3log_{6}(u)+5log_{6}(v)

simplify

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

lo g_{6} (u^{3} v^{5})

Solution steps

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

Apply log rule:

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

3 lo g_{6} (u) = lo g_{6} (u^{3})

= lo g_{6} (u^{3}) + 5 lo g_{6} (v)

Apply log rule:

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

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

= lo g_{6} (u^{3}) + lo g_{6} (v^{5})

Apply log rule:

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

lo g_{6} (u^{3}) + lo g_{6} (v^{5}) = lo g_{6} (u^{3} v^{5})

= lo g_{6} (u^{3} v^{5})

ln (\frac{- 1}{1})

lo g_{10} (4) + lo g_{10} (x)

ln (\frac{125}{8})

2 lo g_{10} (8) + 4 lo g_{10} (x)

What is 3log_{6}(u)+5log_{6}(v) ?
The solution to 3log_{6}(u)+5log_{6}(v) is log_{6}(u^3v^5)