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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

ln (9 x^{3})

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

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

lo g_{5} (\frac{x ^{2}}{x ^{3}})

8 lo g_{9} (x) + 16 lo g_{9} (y)

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