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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (1000) = 3

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

ln (10) - ln (6)

ln (10) - ln (8)

2 - \frac{1}{2} lo g_{n} (4) - lo g_{n} (5)

2 ln (5) + \frac{7}{5} - 2 ln (- 3) - \frac{7}{3}

5 lo g_{10} (a x) + 3 lo g_{10} (a) y

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