What is (log_{c}(x)-log_{c}(y))+7log_{c}(v) ?

The solution to (log_{c}(x)-log_{c}(y))+7log_{c}(v) is log_{c}((xv^7)/y)

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simplify (log_{c}(x)-log_{c}(y))+7log_{c}(v)

simplify

(lo g_{c} (x) - lo g_{c} (y)) + 7 lo g_{c} (v)

lo g_{c} (\frac{x v ^{7}}{y})

Solution steps

(lo g_{c} (x) - lo g_{c} (y)) + 7 lo g_{c} (v)

Apply rule:

(a) = a

(lo g_{c} (x) - lo g_{c} (y)) = lo g_{c} (x) - lo g_{c} (y)

= lo g_{c} (x) - lo g_{c} (y) + 7 lo g_{c} (v)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

7 lo g_{c} (v) = lo g_{c} (v^{7})

= lo g_{c} (x) - lo g_{c} (y) + lo g_{c} (v^{7})

Apply log rule:

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

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

= lo g_{c} (\frac{x}{y}) + lo g_{c} (v^{7})

Apply log rule:

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

lo g_{c} (\frac{x}{y}) + lo g_{c} (v^{7}) = lo g_{c} (\frac{x}{y} v^{7})

= lo g_{c} (\frac{x}{y} v^{7})

Simplify

\frac{x}{y} v^{7} : \frac{x v ^{7}}{y}

= lo g_{c} (\frac{x v ^{7}}{y})

10 lo g_{6} (x) - 2 lo g_{6} (y)

lo g_{10} (23 pq)

lo g_{b} (\frac{32}{125})

- 5 ln (x) - 9 ln (y) + \frac{1}{9} ln (z)

lo g_{10} (\frac{z ^{3}}{x ^{2} y ^{5}})

What is (log_{c}(x)-log_{c}(y))+7log_{c}(v) ?
The solution to (log_{c}(x)-log_{c}(y))+7log_{c}(v) is log_{c}((xv^7)/y)