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

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

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

simplify

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

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

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

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

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{x ^{2}}{y ^{3}}}{z} : \frac{x ^{2}}{y ^{3} z}

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

ln (5) + \frac{1}{3} ln (64)

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

9 ln (x) - 2 ln (y) + 5 ln (z^{3})

lo g_{4} (\frac{1}{16} x^{2} y^{3})

ln (\frac{5}{3}) + 4

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