What is (log_{b}(x)-log_{b}(y))+3log_{b}(v) ?

The solution to (log_{b}(x)-log_{b}(y))+3log_{b}(v) is log_{b}((xv^3)/y)

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simplify (log_{b}(x)-log_{b}(y))+3log_{b}(v)

simplify

(lo g_{b} (x) - lo g_{b} (y)) + 3 lo g_{b} (v)

lo g_{b} (\frac{x v ^{3}}{y})

Solution steps

(lo g_{b} (x) - lo g_{b} (y)) + 3 lo g_{b} (v)

Apply rule:

(a) = a

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

= lo g_{b} (x) - lo g_{b} (y) + 3 lo g_{b} (v)

Apply log rule:

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

3 lo g_{b} (v) = lo g_{b} (v^{3})

= lo g_{b} (x) - lo g_{b} (y) + lo g_{b} (v^{3})

Apply log rule:

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

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

= lo g_{b} (\frac{x}{y}) + lo g_{b} (v^{3})

Apply log rule:

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

lo g_{b} (\frac{x}{y}) + lo g_{b} (v^{3}) = lo g_{b} (\frac{x}{y} v^{3})

= lo g_{b} (\frac{x}{y} v^{3})

Simplify

\frac{x}{y} v^{3} : \frac{x v ^{3}}{y}

= lo g_{b} (\frac{x v ^{3}}{y})

lo g_{4} (x + 6) + lo g_{4} (x)

lo g_{10} (\frac{( x ^{3} y ^{13} )}{z ^{13}})

ln (\frac{325}{310})

lo g_{10} (7 x) \cdot lo g_{10} (4)

lo g_{10} (50 \cdot 5^{\frac{1}{2}}) + 3 lo g_{10} (99)

What is (log_{b}(x)-log_{b}(y))+3log_{b}(v) ?
The solution to (log_{b}(x)-log_{b}(y))+3log_{b}(v) is log_{b}((xv^3)/y)