What is 3log_{6}(u)+12log_{6}(v) ?

The solution to 3log_{6}(u)+12log_{6}(v) is log_{6}(u^3v^{12})

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simplify 3log_{6}(u)+12log_{6}(v)

simplify

3 lo g_{6} (u) + 12 lo g_{6} (v)

lo g_{6} (u^{3} v^{12})

Solution steps

3 lo g_{6} (u) + 12 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}) + 12 lo g_{6} (v)

Apply log rule:

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

12 lo g_{6} (v) = lo g_{6} (v^{12})

= lo g_{6} (u^{3}) + lo g_{6} (v^{12})

Apply log rule:

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

lo g_{6} (u^{3}) + lo g_{6} (v^{12}) = lo g_{6} (u^{3} v^{12})

= lo g_{6} (u^{3} v^{12})

4.7 + lo g_{10} (\frac{0.5}{0.2})

5 ln (x y)

ln (\frac{6}{3})

ln (\frac{22}{72})

ln (v y) - ln (y)

What is 3log_{6}(u)+12log_{6}(v) ?
The solution to 3log_{6}(u)+12log_{6}(v) is log_{6}(u^3v^{12})