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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{5} (\frac{x ^{4}}{25 y ^{2} z})

lo g_{4} (64 x y)

ln (sin (θ)) - ln (\frac{sin ( θ )}{3})

ln (x) + \frac{1}{2} ln ((\frac{y}{x})^{2} + 2 (\frac{y}{x}) + 2)

ln (\frac{e ^{y}}{2})

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