What is log_{10}((9x^7y)/(x^2y^4)) ?

The solution to log_{10}((9x^7y)/(x^2y^4)) is 2log_{10}(3)+5log_{10}(x)-3log_{10}(y)

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simplify log_{10}((9x^7y)/(x^2y^4))

simplify

lo g_{10} (\frac{9 x ^{7} y}{x ^{2} y ^{4}})

2 lo g_{10} (3) + 5 lo g_{10} (x) - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{9 x ^{7} y}{x ^{2} y ^{4}})

Cancel

\frac{9 x ^{7} y}{x ^{2} y ^{4}} : \frac{9 x ^{5}}{y ^{3}}

= lo g_{10} (\frac{9 x ^{5}}{y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{9 x ^{5}}{y ^{3}}) = lo g_{10} (9 x^{5}) - lo g_{10} (y^{3})

= lo g_{10} (9 x^{5}) - lo g_{10} (y^{3})

lo g_{10} (9 x^{5}) = 2 lo g_{10} (3) + 5 lo g_{10} (x)

lo g_{10} (y^{3}) = 3 lo g_{10} (y)

= 2 lo g_{10} (3) + 5 lo g_{10} (x) - 3 lo g_{10} (y)

2 lo g_{10} (0.1) + lo g_{10} (10) + lo g_{10} (0.001) - 5 lo g_{10} (0.0001)

lo g_{3} (13) + lo g_{3} (y)

\frac{1}{6} lo g_{2} (25) - \frac{1}{3} lo g_{2} (10)

lo g_{2} (165) - lo g_{2} (5)

4 ln (x) + 6 ln (y) - 2 ln (z)

What is log_{10}((9x^7y)/(x^2y^4)) ?
The solution to log_{10}((9x^7y)/(x^2y^4)) is 2log_{10}(3)+5log_{10}(x)-3log_{10}(y)