What is log_{9}(y^3z^4)-log_{9}(y^2z^7) ?

The solution to log_{9}(y^3z^4)-log_{9}(y^2z^7) is log_{9}(y/(z^3))

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simplify log_{9}(y^3z^4)-log_{9}(y^2z^7)

simplify

lo g_{9} (y^{3} z^{4}) - lo g_{9} (y^{2} z^{7})

lo g_{9} (\frac{y}{z ^{3}})

Solution steps

lo g_{9} (y^{3} z^{4}) - lo g_{9} (y^{2} z^{7})

Apply log rule:

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

lo g_{9} (y^{3} z^{4}) - lo g_{9} (y^{2} z^{7}) = lo g_{9} (\frac{y ^{3} z ^{4}}{y ^{2} z ^{7}})

= lo g_{9} (\frac{y ^{3} z ^{4}}{y ^{2} z ^{7}})

Cancel

\frac{y ^{3} z ^{4}}{y ^{2} z ^{7}} : \frac{y}{z ^{3}}

= lo g_{9} (\frac{y}{z ^{3}})

- lo g_{10} (4 \cdot 1 0^{- 2})

lo g_{b} (x y) + lo g_{b} (x z) - lo g_{b} (\frac{x}{yz})

2 lo g_{10} (x) - (3 lo g_{10} (y) + 2 lo g_{10} (z))

ln (x) + 2 ln (y) - ln (z)

What is log_{9}(y^3z^4)-log_{9}(y^2z^7) ?
The solution to log_{9}(y^3z^4)-log_{9}(y^2z^7) is log_{9}(y/(z^3))