What is expand log_{4}((3x)/y) ?

The solution to expand log_{4}((3x)/y) is log_{4}(3)+log_{4}(x)-log_{4}(y)

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expand log_{4}((3x)/y)

expand

lo g_{4} (\frac{3 x}{y})

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

Solution steps

lo g_{4} (\frac{3 x}{y})

Apply log rule:

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

lo g_{4} (\frac{3 x}{y}) = lo g_{4} (3 x) - lo g_{4} (y)

= lo g_{4} (3 x) - lo g_{4} (y)

Apply log rule:

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

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

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

ln (2) + ln (x - 2)

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

ln (\frac{\frac{x}{2}}{x})

ln (\frac{( 1 ) ( 1 ) + 1}{( 1 )})

ln (\frac{150}{100})

What is expand log_{4}((3x)/y) ?
The solution to expand log_{4}((3x)/y) is log_{4}(3)+log_{4}(x)-log_{4}(y)