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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (x^{4} z^{3}) : 4 lo g_{10} (x) + 3 lo g_{10} (z)

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

- lo g_{10} (2 \cdot 1 0^{- 6})

ln (\frac{e ^{4}}{10})

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln ((- 2)^{2} - 9))

- lo g_{10} (2.5 \cdot 1 0^{- 3})

lo g_{10} (lo g_{10} (10000 0^{2 x}))

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