What is log_{a}((y^5w^2)/(x^4z^3)) ?

The solution to log_{a}((y^5w^2)/(x^4z^3)) is 5log_{a}(y)+2log_{a}(w)-4log_{a}(x)-3log_{a}(z)

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simplify log_{a}((y^5w^2)/(x^4z^3))

simplify

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

5 lo g_{a} (y) + 2 lo g_{a} (w) - 4 lo g_{a} (x) - 3 lo g_{a} (z)

Solution steps

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

Apply log rule:

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

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}}) = lo g_{a} (y^{5} w^{2}) - lo g_{a} (x^{4} z^{3})

= lo g_{a} (y^{5} w^{2}) - lo g_{a} (x^{4} z^{3})

lo g_{a} (y^{5} w^{2}) = 5 lo g_{a} (y) + 2 lo g_{a} (w)

lo g_{a} (x^{4} z^{3}) = 4 lo g_{a} (x) + 3 lo g_{a} (z)

= 5 lo g_{a} (y) + 2 lo g_{a} (w) - (4 lo g_{a} (x) + 3 lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

- (4 lo g_{a} (x) + 3 lo g_{a} (z)) = - 4 lo g_{a} (x) - 3 lo g_{a} (z)

= 5 lo g_{a} (y) + 2 lo g_{a} (w) - 4 lo g_{a} (x) - 3 lo g_{a} (z)

ln (3 arccos (x))

lo g_{4} (3) - lo g_{4} (7)

lo g_{25} (\frac{20000}{24}) + 1

lo g_{4} (3) - lo g_{4} (5)

3 lo g_{2} (x) - 4 lo g_{2} (x + 3) + lo g_{2} (y)

What is log_{a}((y^5w^2)/(x^4z^3)) ?
The solution to log_{a}((y^5w^2)/(x^4z^3)) is 5log_{a}(y)+2log_{a}(w)-4log_{a}(x)-3log_{a}(z)