What is log_{10}((x^2y^3)/(wz^4)) ?

The solution to log_{10}((x^2y^3)/(wz^4)) is 2log_{10}(x)+3log_{10}(y)-log_{10}(w)-4log_{10}(z)

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simplify log_{10}((x^2y^3)/(wz^4))

simplify

lo g_{10} (\frac{x ^{2} y ^{3}}{w z ^{4}})

2 lo g_{10} (x) + 3 lo g_{10} (y) - lo g_{10} (w) - 4 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{2} y ^{3}}{w z ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} y ^{3}}{w z ^{4}}) = lo g_{10} (x^{2} y^{3}) - lo g_{10} (w z^{4})

= lo g_{10} (x^{2} y^{3}) - lo g_{10} (w z^{4})

lo g_{10} (x^{2} y^{3}) = 2 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{10} (w z^{4}) = lo g_{10} (w) + 4 lo g_{10} (z)

= 2 lo g_{10} (x) + 3 lo g_{10} (y) - (lo g_{10} (w) + 4 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (w) + 4 lo g_{10} (z)) = - lo g_{10} (w) - 4 lo g_{10} (z)

= 2 lo g_{10} (x) + 3 lo g_{10} (y) - lo g_{10} (w) - 4 lo g_{10} (z)

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

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

x^{2} - 2 ln (8 x)

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

lo g_{3} (\frac{1}{9} m n^{2})

What is log_{10}((x^2y^3)/(wz^4)) ?
The solution to log_{10}((x^2y^3)/(wz^4)) is 2log_{10}(x)+3log_{10}(y)-log_{10}(w)-4log_{10}(z)