What is log_{10}(rs)-3log_{10}(p)+7 ?

The solution to log_{10}(rs)-3log_{10}(p)+7 is log_{10}((rs)/(p^3))+7

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simplify log_{10}(rs)-3log_{10}(p)+7

simplify

lo g_{10} (rs) - 3 lo g_{10} (p) + 7

lo g_{10} (\frac{rs}{p ^{3}}) + 7

Solution steps

lo g_{10} (rs) - 3 lo g_{10} (p) + 7

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{10} (p) = lo g_{10} (p^{3})

= lo g_{10} (rs) - lo g_{10} (p^{3}) + 7

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

= lo g_{10} (\frac{rs}{p ^{3}}) + 7

ln (2) + ln (3)

5 ln (x) + ln (x + 1)

lo g_{10} (2) + 2 lo g_{10} (3) + 1

lo g_{5} (3) + 2 lo g_{5} (x)

What is log_{10}(rs)-3log_{10}(p)+7 ?
The solution to log_{10}(rs)-3log_{10}(p)+7 is log_{10}((rs)/(p^3))+7