What is log_{n}((2a)/(7y)) ?

The solution to log_{n}((2a)/(7y)) is log_{n}(2)+log_{n}(a)-log_{n}(7)-log_{n}(y)

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simplify log_{n}((2a)/(7y))

simplify

lo g_{n} (\frac{2 a}{7 y})

lo g_{n} (2) + lo g_{n} (a) - lo g_{n} (7) - lo g_{n} (y)

Solution steps

lo g_{n} (\frac{2 a}{7 y})

Apply log rule:

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

lo g_{n} (\frac{2 a}{7 y}) = lo g_{n} (2 a) - lo g_{n} (7 y)

= lo g_{n} (2 a) - lo g_{n} (7 y)

lo g_{n} (2 a) = lo g_{n} (2) + lo g_{n} (a)

lo g_{n} (7 y) = lo g_{n} (7) + lo g_{n} (y)

= lo g_{n} (2) + lo g_{n} (a) - (lo g_{n} (7) + lo g_{n} (y))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{n} (7) + lo g_{n} (y)) = - lo g_{n} (7) - lo g_{n} (y)

= lo g_{n} (2) + lo g_{n} (a) - lo g_{n} (7) - lo g_{n} (y)

4 lo g_{2} (x) - 5 lo g_{2} (y)

lo g_{b} (\frac{a ^{3} c ^{4}}{a})

lo g_{5} (x) + lo g_{5} (10) + lo g_{5} (y)

ln (a) + 2 ln (a + b) - 4 ln (ab)

lo g_{9} (4) + lo g_{9} (5)

What is log_{n}((2a)/(7y)) ?
The solution to log_{n}((2a)/(7y)) is log_{n}(2)+log_{n}(a)-log_{n}(7)-log_{n}(y)