What is log_{10}((z^5y^4)/(x^5)) ?

The solution to log_{10}((z^5y^4)/(x^5)) is 5log_{10}(z)+4log_{10}(y)-5log_{10}(x)

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simplify log_{10}((z^5y^4)/(x^5))

simplify

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

5 lo g_{10} (z) + 4 lo g_{10} (y) - 5 lo g_{10} (x)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{z ^{5} y ^{4}}{x ^{5}}) = lo g_{10} (z^{5} y^{4}) - lo g_{10} (x^{5})

= lo g_{10} (z^{5} y^{4}) - lo g_{10} (x^{5})

lo g_{10} (z^{5} y^{4}) = 5 lo g_{10} (z) + 4 lo g_{10} (y)

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

= 5 lo g_{10} (z) + 4 lo g_{10} (y) - 5 lo g_{10} (x)

ln (x^{2} + 9 x + 18) - ln (x + 6)

ln (\frac{25}{3})

ln (x + 3) - ln (x)

4.74 + lo g_{10} (\frac{0.3}{0.2})

- lo g_{10} (1.8 \cdot 1 0^{- 5}) - lo g_{10} (0.465)

What is log_{10}((z^5y^4)/(x^5)) ?
The solution to log_{10}((z^5y^4)/(x^5)) is 5log_{10}(z)+4log_{10}(y)-5log_{10}(x)