What is log_{c}(m)-log_{c}(n)-log_{c}(z) ?

The solution to log_{c}(m)-log_{c}(n)-log_{c}(z) is log_{c}(m/(nz))

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simplify log_{c}(m)-log_{c}(n)-log_{c}(z)

simplify

lo g_{c} (m) - lo g_{c} (n) - lo g_{c} (z)

lo g_{c} (\frac{m}{n z})

Solution steps

lo g_{c} (m) - lo g_{c} (n) - lo g_{c} (z)

Apply log rule:

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

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

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

Apply log rule:

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

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

= lo g_{c} (\frac{\frac{m}{n}}{z})

Simplify

\frac{\frac{m}{n}}{z} : \frac{m}{n z}

= lo g_{c} (\frac{m}{n z})

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

ln (x^{3} + 8) - ln (x + 2) - 2 ln (x^{2} - 2 x + 4)

ln (x + 2) - ln (5 x)

lo g_{2} (8 x^{5})

What is log_{c}(m)-log_{c}(n)-log_{c}(z) ?
The solution to log_{c}(m)-log_{c}(n)-log_{c}(z) is log_{c}(m/(nz))