What is log_{10}(r)-log_{10}(p)-log_{10}(q) ?

The solution to log_{10}(r)-log_{10}(p)-log_{10}(q) is log_{10}(r/(pq))

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simplify log_{10}(r)-log_{10}(p)-log_{10}(q)

simplify

lo g_{10} (r) - lo g_{10} (p) - lo g_{10} (q)

lo g_{10} (\frac{r}{pq})

Solution steps

lo g_{10} (r) - lo g_{10} (p) - lo g_{10} (q)

Apply log rule:

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

lo g_{10} (r) - lo g_{10} (p) = lo g_{10} (\frac{r}{p})

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

Apply log rule:

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

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

= lo g_{10} (\frac{\frac{r}{p}}{q})

Simplify

\frac{\frac{r}{p}}{q} : \frac{r}{pq}

= lo g_{10} (\frac{r}{pq})

lo g_{4} (x z)

- \frac{3}{4} \cdot lo g_{2} (\frac{3}{4}) - \frac{1}{4} \cdot lo g_{2} (\frac{1}{4})

lo g_{10} (\frac{x ^{3}}{y})

lo g_{10} (12 x^{4}) - lo g_{10} (4 x)

lo g_{2} (\frac{16}{y})

What is log_{10}(r)-log_{10}(p)-log_{10}(q) ?
The solution to log_{10}(r)-log_{10}(p)-log_{10}(q) is log_{10}(r/(pq))