簡約 log_{10}((sqrt(m^2+n^2))/(100000))

解

簡約

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

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

解答ステップ

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

対数の規則を適用する:

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