What is 5log_{6}(a)+2log_{6}(b) ?

The solution to 5log_{6}(a)+2log_{6}(b) is log_{6}(a^5b^2)

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simplify 5log_{6}(a)+2log_{6}(b)

simplify

5 lo g_{6} (a) + 2 lo g_{6} (b)

lo g_{6} (a^{5} b^{2})

Solution steps

5 lo g_{6} (a) + 2 lo g_{6} (b)

Apply log rule:

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

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

= lo g_{6} (a^{5}) + 2 lo g_{6} (b)

Apply log rule:

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

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

= lo g_{6} (a^{5}) + lo g_{6} (b^{2})

Apply log rule:

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

lo g_{6} (a^{5}) + lo g_{6} (b^{2}) = lo g_{6} (a^{5} b^{2})

= lo g_{6} (a^{5} b^{2})

lo g_{\frac{n}{4}} (\frac{3 n}{4})

lo g_{10} (y^{7} x)

lo g_{2} (x) - lo g_{2} (y) - lo g_{2} (z)

ln (\frac{4}{a ^{2} b}) 3

lo g_{3} (\frac{27}{x + 9})

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