What is log_{9}((ab)/(cd)) ?

The solution to log_{9}((ab)/(cd)) is log_{9}(a)+log_{9}(b)-log_{9}(c)-log_{9}(d)

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simplify log_{9}((ab)/(cd))

simplify

lo g_{9} (\frac{ab}{c d})

lo g_{9} (a) + lo g_{9} (b) - lo g_{9} (c) - lo g_{9} (d)

Solution steps

lo g_{9} (\frac{ab}{c d})

Apply log rule:

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

lo g_{9} (\frac{ab}{c d}) = lo g_{9} (ab) - lo g_{9} (c d)

= lo g_{9} (ab) - lo g_{9} (c d)

lo g_{9} (ab) = lo g_{9} (a) + lo g_{9} (b)

lo g_{9} (c d) = lo g_{9} (c) + lo g_{9} (d)

= lo g_{9} (a) + lo g_{9} (b) - (lo g_{9} (c) + lo g_{9} (d))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{9} (c) + lo g_{9} (d)) = - lo g_{9} (c) - lo g_{9} (d)

= lo g_{9} (a) + lo g_{9} (b) - lo g_{9} (c) - lo g_{9} (d)

lo g_{10} (\frac{p}{q})

ln (\frac{1}{θ})

ln (\frac{27}{8})

lo g_{b} (y z^{7})

lo g_{10} (3) + lo g_{10} (8)

What is log_{9}((ab)/(cd)) ?
The solution to log_{9}((ab)/(cd)) is log_{9}(a)+log_{9}(b)-log_{9}(c)-log_{9}(d)