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

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

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

simplify

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

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

Solution steps

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

Simplify

x^{2} \frac{y}{z} : \frac{x ^{2} y}{z}

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

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

Simplify

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

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

lo g_{a} (\frac{x ^{2}}{y z ^{7}})

lo g_{10} (6) + 4 lo g_{10} (x)

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

lo g_{5} (25 x^{2})

ln (4) + ln (x) - 3 ln (2)

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