What is (log_{b}(x)-log_{b}(y))+6log_{b}(v) ?

The solution to (log_{b}(x)-log_{b}(y))+6log_{b}(v) is log_{b}((xv^6)/y)

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simplify (log_{b}(x)-log_{b}(y))+6log_{b}(v)

simplify

(lo g_{b} (x) - lo g_{b} (y)) + 6 lo g_{b} (v)

lo g_{b} (\frac{x v ^{6}}{y})

Solution steps

(lo g_{b} (x) - lo g_{b} (y)) + 6 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) + 6 lo g_{b} (v)

Apply log rule:

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

6 lo g_{b} (v) = lo g_{b} (v^{6})

= lo g_{b} (x) - lo g_{b} (y) + lo g_{b} (v^{6})

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^{6})

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^{6}) = lo g_{b} (\frac{x}{y} v^{6})

= lo g_{b} (\frac{x}{y} v^{6})

Simplify

\frac{x}{y} v^{6} : \frac{x v ^{6}}{y}

= lo g_{b} (\frac{x v ^{6}}{y})

\frac{1}{2} (3 ln (3) - ln (2))

5 lo g_{10} (4 x^{2})

5 lo g_{10} (x) - 2 lo g_{10} (x + 7)

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

lo g_{10} (0.1) + lo g_{10} (0.001)

What is (log_{b}(x)-log_{b}(y))+6log_{b}(v) ?
The solution to (log_{b}(x)-log_{b}(y))+6log_{b}(v) is log_{b}((xv^6)/y)