What is 2log_{10}(x)+log_{10}(y)-3log_{10}(z) ?

The solution to 2log_{10}(x)+log_{10}(y)-3log_{10}(z) is log_{10}((x^2y)/(z^3))

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simplify 2log_{10}(x)+log_{10}(y)-3log_{10}(z)

simplify

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

lo g_{10} (\frac{x ^{2} y}{z ^{3}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= lo g_{10} (x^{2} y) - 3 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (x^{2} y) - lo g_{10} (z^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x^{2} y) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{2} y}{z ^{3}})

= lo g_{10} (\frac{x ^{2} y}{z ^{3}})

lo g_{2} (\frac{x ^{3} y ^{2}}{z})

lo g_{3} (x) - lo g_{3} (x^{2})

- 2 ln (5 x)

2 lo g_{3} (5) - lo g_{3} (14) + lo g_{9} (3)

lo g_{10} (18) + lo g_{10} (8) - 2 lo g_{10} (25)

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