What is 3log_{c}(x+3)(log_{c}(z)-4log_{c}(y)) ?

The solution to 3log_{c}(x+3)(log_{c}(z)-4log_{c}(y)) is 3log_{c}(x+3)log_{c}(z/(y^4))

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simplify 3log_{c}(x+3)(log_{c}(z)-4log_{c}(y))

simplify

3 lo g_{c} (x + 3) (lo g_{c} (z) - 4 lo g_{c} (y))

3 lo g_{c} (x + 3) lo g_{c} (\frac{z}{y ^{4}})

Solution steps

3 lo g_{c} (x + 3) (lo g_{c} (z) - 4 lo g_{c} (y))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{c} (y) = lo g_{c} (y^{4})

= 3 lo g_{c} (x + 3) (lo g_{c} (z) - lo g_{c} (y^{4}))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{c} (z) - lo g_{c} (y^{4}) = lo g_{c} (\frac{z}{y ^{4}})

= 3 lo g_{c} (x + 3) lo g_{c} (\frac{z}{y ^{4}})

ln (7) - 2 (ln (4) + ln (32))

3 ln (\frac{5.5}{5})

ln (\frac{1}{( r - 1 ) !})

- ln (∣ x ∣^{3}) + ln (∣ x - 1 ∣^{5}) + c

- ln (\frac{1 - a}{a})

What is 3log_{c}(x+3)(log_{c}(z)-4log_{c}(y)) ?
The solution to 3log_{c}(x+3)(log_{c}(z)-4log_{c}(y)) is 3log_{c}(x+3)log_{c}(z/(y^4))