What is log_{3}(x)-log_{9}(4x) ?

The solution to log_{3}(x)-log_{9}(4x) is log_{3}(x)-2log_{9}(2)-log_{9}(x)

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simplify log_{3}(x)-log_{9}(4x)

simplify

lo g_{3} (x) - lo g_{9} (4 x)

lo g_{3} (x) - 2 lo g_{9} (2) - lo g_{9} (x)

Solution steps

lo g_{3} (x) - lo g_{9} (4 x)

Apply log rule:

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

lo g_{9} (4 x) = lo g_{9} (4) + lo g_{9} (x)

= lo g_{3} (x) - (lo g_{9} (x) + lo g_{9} (4))

lo g_{9} (4) = 2 lo g_{9} (2)

= lo g_{3} (x) - (lo g_{9} (x) + 2 lo g_{9} (2))

- (2 lo g_{9} (2) + lo g_{9} (x)) : - 2 lo g_{9} (2) - lo g_{9} (x)

= lo g_{3} (x) - 2 lo g_{9} (2) - lo g_{9} (x)

4 ln (2 x^{3 y})

ln (\frac{4 x}{3 + x})

ln (\frac{45 - 1}{1})

ln (10 e^{4})

5 ln (\frac{300}{100})

What is log_{3}(x)-log_{9}(4x) ?
The solution to log_{3}(x)-log_{9}(4x) is log_{3}(x)-2log_{9}(2)-log_{9}(x)