What is 3log_{6}(a)+6log_{6}(b) ?

The solution to 3log_{6}(a)+6log_{6}(b) is log_{6}(a^3b^6)

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simplify 3log_{6}(a)+6log_{6}(b)

simplify

3 lo g_{6} (a) + 6 lo g_{6} (b)

lo g_{6} (a^{3} b^{6})

Solution steps

3 lo g_{6} (a) + 6 lo g_{6} (b)

Apply log rule:

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

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

= lo g_{6} (a^{3}) + 6 lo g_{6} (b)

Apply log rule:

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

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

= lo g_{6} (a^{3}) + lo g_{6} (b^{6})

Apply log rule:

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

lo g_{6} (a^{3}) + lo g_{6} (b^{6}) = lo g_{6} (a^{3} b^{6})

= lo g_{6} (a^{3} b^{6})

6 lo g_{6} (z) - \frac{1}{4} lo g_{6} (y) + 7 lo g_{6} (x)

\frac{1}{3} (ln (9) - ln (2))

2 x ln (3 x) - 4 x - 4 ln (3 x) + 8

ln (\frac{x}{1 e ^{6}})

- 160 ln (x) - 160 ln (y)

What is 3log_{6}(a)+6log_{6}(b) ?
The solution to 3log_{6}(a)+6log_{6}(b) is log_{6}(a^3b^6)