What is expand log_{2}(((6xy))/(x^2)) ?

The solution to expand log_{2}(((6xy))/(x^2)) is -log_{2}(x)+log_{2}(6)+log_{2}(y)

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expand log_{2}(((6xy))/(x^2))

expand

lo g_{2} (\frac{( 6 x y )}{x ^{2}})

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

Solution steps

lo g_{2} (\frac{( 6 x y )}{x ^{2}})

Apply log rule:

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

lo g_{2} (\frac{( 6 x y )}{x ^{2}}) = lo g_{2} ((6 x y)) - lo g_{2} (x^{2})

= lo g_{2} (6 x y) - lo g_{2} (x^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{2} (x^{2}) = 2 lo g_{2} (x)

= lo g_{2} (6 x y) - 2 lo g_{2} (x)

Apply log rule:

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

lo g_{2} (6 x y) = lo g_{2} (6) + lo g_{2} (x) + lo g_{2} (y)

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

Simplify

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

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

- lo g_{10} (1.67 \cdot 1 0^{- 5})

ln ((7 x^{3} + 3)^{c o s (x)})

lo g_{10} ((\frac{u ^{6}}{v})^{4})

ln (x - 4) [ln (x - 5) + ln (x + 5)]

ln (\frac{10}{12})

What is expand log_{2}(((6xy))/(x^2)) ?
The solution to expand log_{2}(((6xy))/(x^2)) is -log_{2}(x)+log_{2}(6)+log_{2}(y)