What is log_{10}((mn)/p) ?

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

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simplify log_{10}((mn)/p)

simplify

lo g_{10} (\frac{mn}{p})

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

Solution steps

lo g_{10} (\frac{mn}{p})

Apply log rule:

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

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

= lo g_{10} (mn) - lo g_{10} (p)

Simplify

lo g_{10} (mn) : lo g_{10} (m) + lo g_{10} (n)

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

lo g_{10} (9 x^{5}) + 5 lo g_{10} (\frac{1}{x})

\frac{1}{2} ln (x) - 3 ln (x - 1)

7 ln (x) - \frac{1}{6} ln (y)

ln (\frac{cos ( x )}{cos ( x ) - 1})

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