What is log_{10}(p)-3log_{10}(q)-1/2 log_{10}(n) ?

The solution to log_{10}(p)-3log_{10}(q)-1/2 log_{10}(n) is log_{10}(p/(q^3sqrt(n)))

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simplify log_{10}(p)-3log_{10}(q)-1/2 log_{10}(n)

simplify

lo g_{10} (p) - 3 lo g_{10} (q) - \frac{1}{2} lo g_{10} (n)

lo g_{10} (\frac{p}{q ^{3} n})

Solution steps

lo g_{10} (p) - 3 lo g_{10} (q) - \frac{1}{2} lo g_{10} (n)

- 3 lo g_{10} (q) = - lo g_{10} (q^{3})

- \frac{1}{2} lo g_{10} (n) = - lo g_{10} (n^{\frac{1}{2}})

= lo g_{10} (p) - lo g_{10} (q^{3}) - lo g_{10} (n^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (p) - lo g_{10} (q^{3}) = lo g_{10} (\frac{p}{q ^{3}})

= lo g_{10} (\frac{p}{q ^{3}}) - lo g_{10} (n^{\frac{1}{2}})

Apply log rule:

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

lo g_{10} (\frac{p}{q ^{3}}) - lo g_{10} (n^{\frac{1}{2}}) = lo g_{10} (\frac{\frac{p}{q ^{3}}}{n ^{\frac{1}{2}}})

= lo g_{10} (\frac{\frac{p}{q ^{3}}}{n ^{\frac{1}{2}}})

Simplify

\frac{\frac{p}{q ^{3}}}{n ^{\frac{1}{2}}} : \frac{p}{q ^{3} n ^{\frac{1}{2}}}

= lo g_{10} (\frac{p}{q ^{3} n ^{\frac{1}{2}}})

Apply exponent rule:

a^{\frac{1}{2}} = a

n^{\frac{1}{2}} = n

= lo g_{10} (\frac{p}{q ^{3} n})

lo g_{10} \frac{m}{( \frac{p}{q} )}

20 ln (\frac{1400}{1400 + 100 ( 30 )}) + 9.8 (30)

8 lo g_{3} (x) - 2 lo g_{3} (z) - 7 lo g_{3} (y)

\frac{1}{4} ln (1296) - ln (2)

ln (a e^{- b})

What is log_{10}(p)-3log_{10}(q)-1/2 log_{10}(n) ?
The solution to log_{10}(p)-3log_{10}(q)-1/2 log_{10}(n) is log_{10}(p/(q^3sqrt(n)))