What is log_{10}((sqrt(x^2+y^2))/(10000)) ?

The solution to log_{10}((sqrt(x^2+y^2))/(10000)) is log_{10}(sqrt(x^2+y^2))-4

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simplify log_{10}((sqrt(x^2+y^2))/(10000))

simplify

lo g_{10} (\frac{x ^{2} + y ^{2}}{10000})

lo g_{10} (x^{2} + y^{2}) - 4

Solution steps

lo g_{10} (\frac{x ^{2} + y ^{2}}{10000})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} + y ^{2}}{10000}) = lo g_{10} (x^{2} + y^{2}) - lo g_{10} (10000)

= lo g_{10} (x^{2} + y^{2}) - lo g_{10} (10000)

lo g_{10} (10000) = 4

= lo g_{10} (x^{2} + y^{2}) - 4

lo g_{2} (\frac{( 32 x ^{64} )}{128})

ln (x) - \frac{1}{2} (3 ln (x) + 5 ln (y))

3 ln (4) - 4 ln (3)

ln (x) - [ln (x + 1) + ln (x - 1)]

lo g_{b} (x) + lo g_{b} (y) - lo g_{b} (u)

What is log_{10}((sqrt(x^2+y^2))/(10000)) ?
The solution to log_{10}((sqrt(x^2+y^2))/(10000)) is log_{10}(sqrt(x^2+y^2))-4