What is 2log_{10}(x)+log_{10}(y)-log_{10}(z) ?

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

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simplify 2log_{10}(x)+log_{10}(y)-log_{10}(z)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{10} (x) = lo g_{10} (x^{2})

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

= 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})

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

lo g_{3} (9 x^{4})

lo g_{10} (\frac{10 10 a}{0.1})

ln (\frac{e ^{2}}{6})

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