What is log_{10}(m*(p/q)) ?

The solution to log_{10}(m*(p/q)) is log_{10}(m)+log_{10}(p)-log_{10}(q)

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simplify log_{10}(m*(p/q))

simplify

lo g_{10} (m \cdot (\frac{p}{q}))

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

Solution steps

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

Apply rule:

(a) = a

(\frac{p}{q}) = \frac{p}{q}

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

Simplify

m \frac{p}{q} : \frac{m p}{q}

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

Apply log rule:

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

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

= lo g_{10} (m p) - lo g_{10} (q)

Simplify

lo g_{10} (m p) : lo g_{10} (m) + lo g_{10} (p)

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

lo g_{10} (\frac{x}{10000 y ^{9}})

lo g_{3} (\frac{x}{27})

ln (2 e^{x^{2} + 2 x})

2 ln (x + 2) - 3 ln (x^{2} - 4) + ln (x - 2)

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