What is 2log_{b}(x)-log_{b}(y) ?

The solution to 2log_{b}(x)-log_{b}(y) is log_{b}((x^2)/y)

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simplify 2log_{b}(x)-log_{b}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{b} (x) = lo g_{b} (x^{2})

= lo g_{b} (x^{2}) - 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^{2}) - lo g_{b} (y) = lo g_{b} (\frac{x ^{2}}{y})

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

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

- lo g_{10} (7.3 \cdot 1 0^{- 9})

4 ln (2 z^{2})

(1.0299) \cdot ln (\frac{80}{250}) - (0.41195) ln (\frac{550}{240})

ln (\frac{100 + 150}{150})

What is 2log_{b}(x)-log_{b}(y) ?
The solution to 2log_{b}(x)-log_{b}(y) is log_{b}((x^2)/y)