What is expand log_{2}((5x)/(4y)) ?

The solution to expand log_{2}((5x)/(4y)) is log_{2}(5)+log_{2}(x)-2-log_{2}(y)

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expand log_{2}((5x)/(4y))

expand

lo g_{2} (\frac{5 x}{4 y})

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

Solution steps

lo g_{2} (\frac{5 x}{4 y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

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

lo g_{2} (5 x) = lo g_{2} (5) + lo g_{2} (x), lo g_{2} (4 y) = lo g_{2} (4) + lo g_{2} (y)

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

lo g_{2} (4) = 2

= lo g_{2} (5) + lo g_{2} (x) - (lo g_{2} (y) + 2)

- (2 + lo g_{2} (y)) : - 2 - lo g_{2} (y)

= lo g_{2} (5) + lo g_{2} (x) - 2 - lo g_{2} (y)

4 lo g_{e} (\frac{3}{3})

ln (\frac{- sin ( 4 x ) 4}{cos ( 4 x )})

ln (\frac{1.5}{1})

2 lo g_{a} (C) + 3 lo g_{a} (P) + 1

What is expand log_{2}((5x)/(4y)) ?
The solution to expand log_{2}((5x)/(4y)) is log_{2}(5)+log_{2}(x)-2-log_{2}(y)