What is log_{6}(2/(9z)) ?

The solution to log_{6}(2/(9z)) is log_{6}(2)-2log_{6}(3)-log_{6}(z)

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simplify log_{6}(2/(9z))

simplify

lo g_{6} (\frac{2}{9 z})

lo g_{6} (2) - 2 lo g_{6} (3) - lo g_{6} (z)

Solution steps

lo g_{6} (\frac{2}{9 z})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{6} (\frac{2}{9 z}) = lo g_{6} (2) - lo g_{6} (9 z)

= lo g_{6} (2) - lo g_{6} (9 z)

Simplify

lo g_{6} (9 z) : 2 lo g_{6} (3) + lo g_{6} (z)

= lo g_{6} (2) - (2 lo g_{6} (3) + lo g_{6} (z))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{6} (3) + lo g_{6} (z)) = - 2 lo g_{6} (3) - lo g_{6} (z)

= lo g_{6} (2) - 2 lo g_{6} (3) - lo g_{6} (z)

\frac{1}{2} ln (x) + \frac{1}{2} ln (y)

lo g_{10} (14) + \frac{1}{2} lo g_{10} (3) - lo g_{10} (2)

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

lo g_{10} (7.2) - lo g_{10} (6.7)

ln (12) - ln (5)

What is log_{6}(2/(9z)) ?
The solution to log_{6}(2/(9z)) is log_{6}(2)-2log_{6}(3)-log_{6}(z)