What is log_{10}((sqrt(u^2+v^2))/(100)) ?

The solution to log_{10}((sqrt(u^2+v^2))/(100)) is log_{10}(sqrt(u^2+v^2))-2

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simplify log_{10}((sqrt(u^2+v^2))/(100))

simplify

lo g_{10} (\frac{u ^{2} + v ^{2}}{100})

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

Solution steps

lo g_{10} (\frac{u ^{2} + v ^{2}}{100})

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}}{100}) = lo g_{10} (u^{2} + v^{2}) - lo g_{10} (100)

= lo g_{10} (u^{2} + v^{2}) - lo g_{10} (100)

lo g_{10} (100) = 2

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

\frac{1}{2} (lo g_{3} (s) + lo g_{3} (t))

5 lo g_{10} (x^{3}) - 4 lo g_{10} (x^{2})

lo g_{10} (\frac{y ^{5} x ^{2}}{z ^{5}})

ln (\frac{11}{5})

lo g_{3} (\frac{x ^{2}}{81 y ^{4}})

What is log_{10}((sqrt(u^2+v^2))/(100)) ?
The solution to log_{10}((sqrt(u^2+v^2))/(100)) is log_{10}(sqrt(u^2+v^2))-2