What is log_{10}(1/(sqrt(u^2+v^2))) ?

The solution to log_{10}(1/(sqrt(u^2+v^2))) is -log_{10}(sqrt(u^2+v^2))

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simplify log_{10}(1/(sqrt(u^2+v^2)))

simplify

lo g_{10} (\frac{1}{u ^{2} + v ^{2}})

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

Solution steps

lo g_{10} (\frac{1}{u ^{2} + v ^{2}})

Simplify

\frac{1}{u ^{2} + v ^{2}} : (u^{2} + v^{2})^{- 1}

= lo g_{10} ((u^{2} + v^{2})^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((u^{2} + v^{2})^{- 1}) = - 1 \cdot lo g_{10} (u^{2} + v^{2})

= - 1 \cdot lo g_{10} (u^{2} + v^{2})

Apply rule:

1 \cdot a = a

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

lo g_{10} (x) - 2 \cdot lo g_{10} (y) + 5 \cdot lo g_{10} (z)

lo g_{4} (2) + lo g_{4} (x)

lo g_{3} (\frac{27}{x + 4})

\frac{9}{2} ln (\frac{9}{2})

What is log_{10}(1/(sqrt(u^2+v^2))) ?
The solution to log_{10}(1/(sqrt(u^2+v^2))) is -log_{10}(sqrt(u^2+v^2))