What is 5log_{b}(x)-log_{b}(y) ?

The solution to 5log_{b}(x)-log_{b}(y) is log_{b}((x^5)/y)

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simplify 5log_{b}(x)-log_{b}(y)

simplify

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

lo g_{b} (\frac{x ^{5}}{y})

Solution steps

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

Apply log rule:

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

5 lo g_{b} (x) = lo g_{b} (x^{5})

= lo g_{b} (x^{5}) - 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^{5}) - lo g_{b} (y) = lo g_{b} (\frac{x ^{5}}{y})

= lo g_{b} (\frac{x ^{5}}{y})

- lo g_{10} (2.8 \cdot 1 0^{- 5})

0.9 ln (6) - 2.4 ln (8)

ln (2 x^{\frac{8}{1 - x}})

- lo g_{10} (1.5 \cdot 1 0^{- 5})

- lo g_{10} (1.41 \cdot 1 0^{- 6})

What is 5log_{b}(x)-log_{b}(y) ?
The solution to 5log_{b}(x)-log_{b}(y) is log_{b}((x^5)/y)