What is 2log_{10}(u)-3log_{10}(v)-2log_{10}(z) ?

The solution to 2log_{10}(u)-3log_{10}(v)-2log_{10}(z) is log_{10}((u^2)/(v^3z^2))

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simplify 2log_{10}(u)-3log_{10}(v)-2log_{10}(z)

simplify

2 lo g_{10} (u) - 3 lo g_{10} (v) - 2 lo g_{10} (z)

lo g_{10} (\frac{u ^{2}}{v ^{3} z ^{2}})

Solution steps

2 lo g_{10} (u) - 3 lo g_{10} (v) - 2 lo g_{10} (z)

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

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

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

= lo g_{10} (u^{2}) - lo g_{10} (v^{3}) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (u^{2}) - lo g_{10} (v^{3}) = lo g_{10} (\frac{u ^{2}}{v ^{3}})

= lo g_{10} (\frac{u ^{2}}{v ^{3}}) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (\frac{u ^{2}}{v ^{3}}) - lo g_{10} (z^{2}) = lo g_{10} (\frac{\frac{u ^{2}}{v ^{3}}}{z ^{2}})

= lo g_{10} (\frac{\frac{u ^{2}}{v ^{3}}}{z ^{2}})

Simplify

\frac{\frac{u ^{2}}{v ^{3}}}{z ^{2}} : \frac{u ^{2}}{v ^{3} z ^{2}}

= lo g_{10} (\frac{u ^{2}}{v ^{3} z ^{2}})

lo g_{2} (7) + lo g_{2} (3)

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

9 ln (t) + ln (y) - ln (y + 1)

lo g_{3} (\frac{c}{9})

lo g_{2} (\frac{1}{3}) + lo g_{4} (9)

What is 2log_{10}(u)-3log_{10}(v)-2log_{10}(z) ?
The solution to 2log_{10}(u)-3log_{10}(v)-2log_{10}(z) is log_{10}((u^2)/(v^3z^2))