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

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

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simplify log_{4}((5sqrt(x))/y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{4} (5 x) : lo g_{4} (5) + lo g_{4} (x)

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

lo g_{10} (1000000 y)

lo g_{3} (11 x (3 x + 4))

ln (x^{11} 2 - x)

lo g_{5} (x) - lo g_{5} (x^{6})

lo g_{10} (\frac{x ( x + 4 )}{( x + 3 ) ^{14}})

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