What is log_{10}((x^3y)/z) ?

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

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simplify log_{10}((x^3y)/z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

4 lo g_{10} (\frac{x}{5})

- lo g_{10} (6.5 \cdot 1 0^{- 5})

lo g_{3} (x) + lo g_{3} (x + 8)

- lo g_{10} (7.2 \cdot 1 0^{- 4})

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