What is expand log_{10}((5x)/(4y)) ?

The solution to expand log_{10}((5x)/(4y)) is log_{10}(5)+log_{10}(x)-2log_{10}(2)-log_{10}(y)

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expand log_{10}((5x)/(4y))

expand

lo g_{10} (\frac{5 x}{4 y})

lo g_{10} (5) + lo g_{10} (x) - 2 lo g_{10} (2) - lo g_{10} (y)

Solution steps

lo g_{10} (\frac{5 x}{4 y})

Apply log rule:

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

lo g_{10} (\frac{5 x}{4 y}) = lo g_{10} (5 x) - lo g_{10} (4 y)

= lo g_{10} (5 x) - lo g_{10} (4 y)

Apply log rule:

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

lo g_{10} (5 x) = lo g_{10} (5) + lo g_{10} (x), lo g_{10} (4 y) = lo g_{10} (4) + lo g_{10} (y)

= lo g_{10} (5) + lo g_{10} (x) - (lo g_{10} (y) + lo g_{10} (4))

lo g_{10} (4) = 2 lo g_{10} (2)

= lo g_{10} (5) + lo g_{10} (x) - (lo g_{10} (y) + 2 lo g_{10} (2))

- (2 lo g_{10} (2) + lo g_{10} (y)) : - 2 lo g_{10} (2) - lo g_{10} (y)

= lo g_{10} (5) + lo g_{10} (x) - 2 lo g_{10} (2) - lo g_{10} (y)

ln (\frac{x ^{\frac{1}{2}} ( 2 x + 7 ) ^{4}}{( 3 x ^{2} + 1 ) ^{2}})

lo g_{10} (1000 x^{3} y^{- 5})

lo g_{2} (3) + 4 lo g_{2} (x) - 6 lo g_{2} (y)

7 lo g_{3} (k) + 6 lo g_{3} (m) - 9 lo g_{3} (n)

ln (x^{2} - 9) - ln (2 x^{2} - 5 x - 3) - 2 ln (x + 3)

What is expand log_{10}((5x)/(4y)) ?
The solution to expand log_{10}((5x)/(4y)) is log_{10}(5)+log_{10}(x)-2log_{10}(2)-log_{10}(y)