What is 5log_{6}(u)+2log_{6}(v) ?

The solution to 5log_{6}(u)+2log_{6}(v) is log_{6}(u^5v^2)

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simplify 5log_{6}(u)+2log_{6}(v)

simplify

5 lo g_{6} (u) + 2 lo g_{6} (v)

lo g_{6} (u^{5} v^{2})

Solution steps

5 lo g_{6} (u) + 2 lo g_{6} (v)

Apply log rule:

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

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

= lo g_{6} (u^{5}) + 2 lo g_{6} (v)

Apply log rule:

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

2 lo g_{6} (v) = lo g_{6} (v^{2})

= lo g_{6} (u^{5}) + lo g_{6} (v^{2})

Apply log rule:

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

lo g_{6} (u^{5}) + lo g_{6} (v^{2}) = lo g_{6} (u^{5} v^{2})

= lo g_{6} (u^{5} v^{2})

3 lo g_{4} (u) - 18 lo g_{4} (v)

\frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 ) - lo g _{10} ( 2 )}

ln (\frac{8}{10})

2 (ln (u^{3}) + ln (w^{\frac{1}{3}}) - ln (v))

lo g_{9} (x - 5) + lo g_{9} (x + 5)

What is 5log_{6}(u)+2log_{6}(v) ?
The solution to 5log_{6}(u)+2log_{6}(v) is log_{6}(u^5v^2)