What is log_{10}((1000)/(sqrt(x^2+y^2))) ?

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

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simplify log_{10}((1000)/(sqrt(x^2+y^2)))

simplify

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}})

3 - lo g_{10} (x^{2} + y^{2})

Solution steps

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}})

Apply log rule:

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

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}}) = lo g_{10} (1000) - lo g_{10} (x^{2} + y^{2})

= lo g_{10} (1000) - lo g_{10} (x^{2} + y^{2})

lo g_{10} (1000) = 3

= 3 - lo g_{10} (x^{2} + y^{2})

lo g_{10} (3 x^{5})

ln (\frac{x ^{2}}{25})

- lo g_{10} (1.3 \cdot 1 0^{- 7})

2 ln (x) - 3 (ln (x^{2}) + ln (x))

lo g_{4} (\frac{16}{y})

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