What is log_{10}(((x^9y^5))/((z^3))) ?

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

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simplify log_{10}(((x^9y^5))/((z^3)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

ln (\frac{11782}{1000})

lo g_{3} (x yz)

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

ln (\frac{( \frac{668}{530.5} )}{0.021})

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