What is log_{10}((sqrt(u^2+v^2))/(10000)) ?

The solution to log_{10}((sqrt(u^2+v^2))/(10000)) is log_{10}(sqrt(u^2+v^2))-4

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simplify log_{10}((sqrt(u^2+v^2))/(10000))

simplify

lo g_{10} (\frac{u ^{2} + v ^{2}}{10000})

lo g_{10} (u^{2} + v^{2}) - 4

Solution steps

lo g_{10} (\frac{u ^{2} + v ^{2}}{10000})

Apply log rule:

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

lo g_{10} (\frac{u ^{2} + v ^{2}}{10000}) = lo g_{10} (u^{2} + v^{2}) - lo g_{10} (10000)

= lo g_{10} (u^{2} + v^{2}) - lo g_{10} (10000)

lo g_{10} (10000) = 4

= lo g_{10} (u^{2} + v^{2}) - 4

- lo g_{10} (2.3 \cdot 1 0^{- 5})

lo g_{10} (\frac{x ^{2} - 1}{y z ^{3}})

4 \cdot lo g_{0.1} (3) - \frac{2}{3} \cdot lo g_{0.1} (27) + 2 \cdot lo g_{0.1} (6)

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

ln (\frac{1}{8}) - ln (\frac{1}{2})

What is log_{10}((sqrt(u^2+v^2))/(10000)) ?
The solution to log_{10}((sqrt(u^2+v^2))/(10000)) is log_{10}(sqrt(u^2+v^2))-4