What is log_{10}((1000)/(sqrt(m^2+n^2))) ?

The solution to log_{10}((1000)/(sqrt(m^2+n^2))) is 3-log_{10}(sqrt(m^2+n^2))

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simplify log_{10}((1000)/(sqrt(m^2+n^2)))

simplify

lo g_{10} (\frac{1000}{m ^{2} + n ^{2}})

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

Solution steps

lo g_{10} (\frac{1000}{m ^{2} + n ^{2}})

Apply log rule:

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

lo g_{10} (\frac{1000}{m ^{2} + n ^{2}}) = lo g_{10} (1000) - lo g_{10} (m^{2} + n^{2})

= lo g_{10} (1000) - lo g_{10} (m^{2} + n^{2})

lo g_{10} (1000) = 3

= 3 - lo g_{10} (m^{2} + n^{2})

lo g_{4} (3 x y)

5 lo g_{5} (x) - \frac{1}{4} lo g_{5} (8 - x)

lo g_{10} (d) - 4 lo g_{10} (g)

lo g_{6} (\frac{2 y - 3}{y})

lo g_{b} (5) + 3 lo g_{b} (10) - lo g_{b} (40)

What is log_{10}((1000)/(sqrt(m^2+n^2))) ?
The solution to log_{10}((1000)/(sqrt(m^2+n^2))) is 3-log_{10}(sqrt(m^2+n^2))