What is (log_{c}(x)-log_{c}(y))+2log_{c}(v) ?

The solution to (log_{c}(x)-log_{c}(y))+2log_{c}(v) is log_{c}((xv^2)/y)

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simplify (log_{c}(x)-log_{c}(y))+2log_{c}(v)

simplify

(lo g_{c} (x) - lo g_{c} (y)) + 2 lo g_{c} (v)

lo g_{c} (\frac{x v ^{2}}{y})

Solution steps

(lo g_{c} (x) - lo g_{c} (y)) + 2 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) + 2 lo g_{c} (v)

Apply log rule:

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

2 lo g_{c} (v) = lo g_{c} (v^{2})

= lo g_{c} (x) - lo g_{c} (y) + lo g_{c} (v^{2})

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^{2})

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^{2}) = lo g_{c} (\frac{x}{y} v^{2})

= lo g_{c} (\frac{x}{y} v^{2})

Simplify

\frac{x}{y} v^{2} : \frac{x v ^{2}}{y}

= lo g_{c} (\frac{x v ^{2}}{y})

ln (\frac{1}{2.7})

2 ln (\frac{401}{2})

\frac{6}{7} lo g_{2} (\frac{6}{7}) + \frac{1}{7} lo g_{2} (\frac{1}{7})

3 ln (\frac{7}{2}) + 10

lo g_{10} (\frac{( 3 x ^{2} ) ^{4}}{( 9 x ^{8} ) ^{\frac{1}{2}}})

What is (log_{c}(x)-log_{c}(y))+2log_{c}(v) ?
The solution to (log_{c}(x)-log_{c}(y))+2log_{c}(v) is log_{c}((xv^2)/y)