What is log_{6}(1/6 mn^2) ?

The solution to log_{6}(1/6 mn^2) is -1+log_{6}(m)+2log_{6}(n)

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simplify log_{6}(1/6 mn^2)

simplify

lo g_{6} (\frac{1}{6} m n^{2})

- 1 + lo g_{6} (m) + 2 lo g_{6} (n)

Solution steps

lo g_{6} (\frac{1}{6} m n^{2})

\frac{1}{6} = 6^{- 1}

= lo g_{6} (6^{- 1} m n^{2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{6} (6^{- 1} m n^{2}) = lo g_{6} (6^{- 1}) + lo g_{6} (m n^{2})

= lo g_{6} (6^{- 1}) + lo g_{6} (m n^{2})

Apply log rule:

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

lo g_{6} (6^{- 1}) = - 1

= - 1 + lo g_{6} (m n^{2})

Simplify

lo g_{6} (m n^{2}) : lo g_{6} (m) + 2 lo g_{6} (n)

= - 1 + (lo g_{6} (m) + 2 lo g_{6} (n))

Apply rule:

a + (b + c) = a + b + c

- 1 + (lo g_{6} (m) + 2 lo g_{6} (n)) = - 1 + lo g_{6} (m) + 2 lo g_{6} (n)

= - 1 + lo g_{6} (m) + 2 lo g_{6} (n)

ln (\frac{e ^{2}}{10})

lo g_{a} (8) + lo g_{a} (5)

\frac{2 ln ( 2 )}{ln ( \frac{2}{3} )}

lo g_{3} (7) + lo g_{3} (12) - lo g_{3} (4)

ln (\frac{e ^{9}}{10})

What is log_{6}(1/6 mn^2) ?
The solution to log_{6}(1/6 mn^2) is -1+log_{6}(m)+2log_{6}(n)