What is expand log_{4}((y^8)/(16x)) ?

The solution to expand log_{4}((y^8)/(16x)) is 8log_{4}(y)-2-log_{4}(x)

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expand log_{4}((y^8)/(16x))

expand

lo g_{4} (\frac{y ^{8}}{16 x})

8 lo g_{4} (y) - 2 - lo g_{4} (x)

Solution steps

lo g_{4} (\frac{y ^{8}}{16 x})

Apply log rule:

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

lo g_{4} (\frac{y ^{8}}{16 x}) = lo g_{4} (y^{8}) - lo g_{4} (16 x)

= lo g_{4} (y^{8}) - lo g_{4} (16 x)

Apply log rule:

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

lo g_{4} (y^{8}) = 8 lo g_{4} (y)

= 8 lo g_{4} (y) - lo g_{4} (16 x)

Apply log rule:

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

lo g_{4} (16 x) = lo g_{4} (16) + lo g_{4} (x)

= 8 lo g_{4} (y) - (lo g_{4} (x) + lo g_{4} (16))

lo g_{4} (16) = 2

= 8 lo g_{4} (y) - (lo g_{4} (x) + 2)

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

= 8 lo g_{4} (y) - 2 - lo g_{4} (x)

6 lo g_{5} (x) + 2 lo g_{5} (4 x) - \frac{1}{5} lo g_{5} (4 - x)

lo g_{x} (\frac{yz}{w})

- \frac{1}{3} ln (\frac{9}{19})

16.7 + 10 \cdot lo g_{10} (\frac{450}{70})

2 ln (x) + \frac{1}{3} ln (x + 5)

What is expand log_{4}((y^8)/(16x)) ?
The solution to expand log_{4}((y^8)/(16x)) is 8log_{4}(y)-2-log_{4}(x)