What is log_{4}((4x^6)/y) ?

The solution to log_{4}((4x^6)/y) is 1+6log_{4}(x)-log_{4}(y)

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simplify log_{4}((4x^6)/y)

simplify

lo g_{4} (\frac{4 x ^{6}}{y})

1 + 6 lo g_{4} (x) - lo g_{4} (y)

Solution steps

lo g_{4} (\frac{4 x ^{6}}{y})

Apply log rule:

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

lo g_{4} (\frac{4 x ^{6}}{y}) = lo g_{4} (4 x^{6}) - lo g_{4} (y)

= lo g_{4} (4 x^{6}) - lo g_{4} (y)

Simplify

lo g_{4} (4 x^{6}) : 1 + 6 lo g_{4} (x)

= 1 + 6 lo g_{4} (x) - lo g_{4} (y)

ln (\frac{e ^{4}}{6})

ln (2 x) + 1

lo g_{b} (\frac{1}{6})

What is log_{4}((4x^6)/y) ?
The solution to log_{4}((4x^6)/y) is 1+6log_{4}(x)-log_{4}(y)