What is log_{9}(x^8)-log_{9}(x^5) ?

The solution to log_{9}(x^8)-log_{9}(x^5) is 3log_{9}(x)

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simplify log_{9}(x^8)-log_{9}(x^5)

simplify

lo g_{9} (x^{8}) - lo g_{9} (x^{5})

3 lo g_{9} (x)

Solution steps

lo g_{9} (x^{8}) - lo g_{9} (x^{5})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{9} (x^{8}) = 8 lo g_{9} (x)

= 8 lo g_{9} (x) - lo g_{9} (x^{5})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{9} (x^{5}) = 5 lo g_{9} (x)

= 8 lo g_{9} (x) - 5 lo g_{9} (x)

Add similar elements:

8 lo g_{9} (x) - 5 lo g_{9} (x) = 3 lo g_{9} (x)

= 3 lo g_{9} (x)

lo g_{10} (a \cdot b)

ln (3 x^{4})

lo g_{10} (3 x^{2})

lo g_{2} (\frac{16}{x - 1})

\frac{1}{2} lo g_{10} (3)

What is log_{9}(x^8)-log_{9}(x^5) ?
The solution to log_{9}(x^8)-log_{9}(x^5) is 3log_{9}(x)