What is log_{10}(m)-log_{10}(n)+log_{10}(p) ?

The solution to log_{10}(m)-log_{10}(n)+log_{10}(p) is log_{10}((mp)/n)

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simplify log_{10}(m)-log_{10}(n)+log_{10}(p)

simplify

lo g_{10} (m) - lo g_{10} (n) + lo g_{10} (p)

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

Solution steps

lo g_{10} (m) - lo g_{10} (n) + lo g_{10} (p)

Apply log rule:

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

lo g_{10} (m) - lo g_{10} (n) = lo g_{10} (\frac{m}{n})

= lo g_{10} (\frac{m}{n}) + lo g_{10} (p)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{m}{n}) + lo g_{10} (p) = lo g_{10} (\frac{m}{n} p)

= lo g_{10} (\frac{m}{n} p)

Simplify

\frac{m}{n} p : \frac{m p}{n}

= lo g_{10} (\frac{m p}{n})

ln (\frac{x}{1 + x})

lo g_{a} (7 x - 4) - lo g_{a} (5 x + 2)

- lo g_{10} (1.6 \cdot 1 0^{- 5})

ln (\frac{e ^{8}}{15})

ln (x^{4} - 1) - ln (x^{2} - 1)

What is log_{10}(m)-log_{10}(n)+log_{10}(p) ?
The solution to log_{10}(m)-log_{10}(n)+log_{10}(p) is log_{10}((mp)/n)