What is log_{10}((x^2y)/(w^5z)) ?

The solution to log_{10}((x^2y)/(w^5z)) is 2log_{10}(x)+log_{10}(y)-5log_{10}(w)-log_{10}(z)

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simplify log_{10}((x^2y)/(w^5z))

simplify

lo g_{10} (\frac{x ^{2} y}{w ^{5} z})

2 lo g_{10} (x) + lo g_{10} (y) - 5 lo g_{10} (w) - lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{2} y}{w ^{5} z})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} y}{w ^{5} z}) = lo g_{10} (x^{2} y) - lo g_{10} (w^{5} z)

= lo g_{10} (x^{2} y) - lo g_{10} (w^{5} z)

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

lo g_{10} (w^{5} z) = 5 lo g_{10} (w) + lo g_{10} (z)

= 2 lo g_{10} (x) + lo g_{10} (y) - (5 lo g_{10} (w) + lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (5 lo g_{10} (w) + lo g_{10} (z)) = - 5 lo g_{10} (w) - lo g_{10} (z)

= 2 lo g_{10} (x) + lo g_{10} (y) - 5 lo g_{10} (w) - lo g_{10} (z)

- lo g_{2} (\frac{3}{8})

- lo g_{10} (5.4 \cdot 1 0^{- 4})

ln (2 + e^{1}) - ln (2 + e^{- 3})

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 6)

What is log_{10}((x^2y)/(w^5z)) ?
The solution to log_{10}((x^2y)/(w^5z)) is 2log_{10}(x)+log_{10}(y)-5log_{10}(w)-log_{10}(z)