What is expand log_{4}((xsqrt(z))/(16y^2)) ?

The solution to expand log_{4}((xsqrt(z))/(16y^2)) is log_{4}(x)+log_{4}(sqrt(z))-2-2log_{4}(y)

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expand log_{4}((xsqrt(z))/(16y^2))

expand

lo g_{4} (\frac{x z}{16 y ^{2}})

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

Solution steps

lo g_{4} (\frac{x z}{16 y ^{2}})

Apply log rule:

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

lo g_{4} (\frac{x z}{16 y ^{2}}) = lo g_{4} (x z) - lo g_{4} (16 y^{2})

= lo g_{4} (x z) - lo g_{4} (16 y^{2})

Apply log rule:

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

lo g_{4} (x z) = lo g_{4} (x) + lo g_{4} (z), lo g_{4} (16 y^{2}) = lo g_{4} (16) + lo g_{4} (y^{2})

= lo g_{4} (x) + lo g_{4} (z) - (lo g_{4} (y^{2}) + lo g_{4} (16))

Apply log rule:

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

lo g_{4} (y^{2}) = 2 lo g_{4} (y)

= lo g_{4} (x) + lo g_{4} (z) - (lo g_{4} (16) + 2 lo g_{4} (y))

lo g_{4} (16) = 2

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

- (2 + 2 lo g_{4} (y)) : - 2 - 2 lo g_{4} (y)

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

ln (\frac{4}{6}) - ln (\frac{1}{3})

f (x) = ln (\frac{3}{3 - x})

2 ln (x) - 2 ln (y)

ln (i e^{π})

- ln ∣ 8 - 3 ∣ + 2 ln ∣ 8 - 2 ∣

What is expand log_{4}((xsqrt(z))/(16y^2)) ?
The solution to expand log_{4}((xsqrt(z))/(16y^2)) is log_{4}(x)+log_{4}(sqrt(z))-2-2log_{4}(y)