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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- ln (\frac{41}{160})

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

\frac{1}{3} lo g_{4} (x) + lo g_{4} (z)

- lo g_{10} (5 x 1 0^{- 4})

3 ln (x) - ln (x + 6) - ln (x - 6)

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