What is log_{b}((4y^5)/(x^4z)) ?

The solution to log_{b}((4y^5)/(x^4z)) is 2log_{b}(2)+5log_{b}(y)-4log_{b}(x)-log_{b}(z)

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simplify log_{b}((4y^5)/(x^4z))

simplify

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

2 lo g_{b} (2) + 5 lo g_{b} (y) - 4 lo g_{b} (x) - lo g_{b} (z)

Solution steps

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

Apply log rule:

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

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

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

lo g_{b} (4 y^{5}) = 2 lo g_{b} (2) + 5 lo g_{b} (y)

lo g_{b} (x^{4} z) = 4 lo g_{b} (x) + lo g_{b} (z)

= 2 lo g_{b} (2) + 5 lo g_{b} (y) - (4 lo g_{b} (x) + lo g_{b} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= 2 lo g_{b} (2) + 5 lo g_{b} (y) - 4 lo g_{b} (x) - lo g_{b} (z)

ln (\frac{x ( 3 x - 2 ) ^{5}}{3 - 5 x})

lo g_{4} (6) + 2 lo g_{4} (3)

lo g_{5} (2) - lo g_{5} (t)

lo g_{8} (k^{2} - 64) - lo g_{8} (k) - 8

What is log_{b}((4y^5)/(x^4z)) ?
The solution to log_{b}((4y^5)/(x^4z)) is 2log_{b}(2)+5log_{b}(y)-4log_{b}(x)-log_{b}(z)