What is log_{10}((x^2y^2)/z) ?

The solution to log_{10}((x^2y^2)/z) is 2log_{10}(x)+2log_{10}(y)-log_{10}(z)

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simplify log_{10}((x^2y^2)/z)

simplify

lo g_{10} (\frac{x ^{2} y ^{2}}{z})

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

Solution steps

lo g_{10} (\frac{x ^{2} y ^{2}}{z})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} y ^{2}}{z}) = lo g_{10} (x^{2} y^{2}) - lo g_{10} (z)

= lo g_{10} (x^{2} y^{2}) - lo g_{10} (z)

Simplify

lo g_{10} (x^{2} y^{2}) : 2 lo g_{10} (x) + 2 lo g_{10} (y)

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

lo g_{10} (0.1) + lo g_{10} (0.001)

lo g_{10} (\frac{1000}{p ^{2} + 9})

2 ln (x) - ln (x - y) + 2 ln (y)

8.1 + lo g_{10} (\frac{0.11 + 0.03}{0.18 - 0.03})

ln (\frac{1}{x} y^{\frac{( 1 - x )}{x}})

What is log_{10}((x^2y^2)/z) ?
The solution to log_{10}((x^2y^2)/z) is 2log_{10}(x)+2log_{10}(y)-log_{10}(z)