What is log_{10}(r^2sqrt(s))-log_{10}(rs^2)+1 ?

The solution to log_{10}(r^2sqrt(s))-log_{10}(rs^2)+1 is log_{10}(r/(ssqrt(s)))+1

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simplify log_{10}(r^2sqrt(s))-log_{10}(rs^2)+1

simplify

lo g_{10} (r^{2} s) - lo g_{10} (r s^{2}) + 1

lo g_{10} (\frac{r}{s s}) + 1

Solution steps

lo g_{10} (r^{2} s) - lo g_{10} (r s^{2}) + 1

Apply log rule:

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

lo g_{10} (r^{2} s) - lo g_{10} (r s^{2}) = lo g_{10} (\frac{r ^{2} s}{r s ^{2}})

= lo g_{10} (\frac{r ^{2} s}{r s ^{2}}) + 1

Cancel

\frac{r ^{2} s}{r s ^{2}} : \frac{r}{s s}

= lo g_{10} (\frac{r}{s s}) + 1

lo g_{5} (x^{2}) - lo g_{5} (2)

lo g_{3} (\frac{1}{2}) - lo g_{9} (\frac{1}{2})

lo g_{2} (\frac{i}{j s})

ln (\frac{u}{3} + 1) - ln (\frac{u}{3} - 1)

lo g_{7} (9 x)

What is log_{10}(r^2sqrt(s))-log_{10}(rs^2)+1 ?
The solution to log_{10}(r^2sqrt(s))-log_{10}(rs^2)+1 is log_{10}(r/(ssqrt(s)))+1