What is log_{10}((sqrt(m^2+n^2))/(100000)) ?

The solution to log_{10}((sqrt(m^2+n^2))/(100000)) is log_{10}(sqrt(m^2+n^2))-5

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simplify log_{10}((sqrt(m^2+n^2))/(100000))

simplify

lo g_{10} (\frac{m ^{2} + n ^{2}}{100000})

lo g_{10} (m^{2} + n^{2}) - 5

Solution steps

lo g_{10} (\frac{m ^{2} + n ^{2}}{100000})

Apply log rule:

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

lo g_{10} (\frac{m ^{2} + n ^{2}}{100000}) = lo g_{10} (m^{2} + n^{2}) - lo g_{10} (100000)

= lo g_{10} (m^{2} + n^{2}) - lo g_{10} (100000)

lo g_{10} (100000) = 5

= lo g_{10} (m^{2} + n^{2}) - 5

ln (x + 5) + ln (x - 5)

lo g_{10} (\frac{7 x}{2})

lo g_{3} (9 x^{5})

ln (a + b) + ln (a - b) - 7 ln (c)

What is log_{10}((sqrt(m^2+n^2))/(100000)) ?
The solution to log_{10}((sqrt(m^2+n^2))/(100000)) is log_{10}(sqrt(m^2+n^2))-5