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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{a} (y^{2} z^{4}) = 2 lo g_{a} (y) + 4 lo g_{a} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

- lo g_{10} (1.4 \cdot 1 0^{- 5})

\frac{1}{2} lo g_{10} (x) + 5 lo g_{10} (y)

(lo g_{b} (x) - lo g_{b} (y)) + 7 lo g_{b} (v)

4 ln (x) + 3 ln (y) - 2 ln (z)

lo g_{2} (16 x^{3})

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