What is log_{2}(x^3)-log_{2}(x^2) ?

The solution to log_{2}(x^3)-log_{2}(x^2) is log_{2}(x)

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simplify log_{2}(x^3)-log_{2}(x^2)

simplify

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

lo g_{2} (x)

Solution steps

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

Apply log rule

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

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

= 3 lo g_{2} (x) - lo g_{2} (x^{2})

Apply log rule

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

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

= 3 lo g_{2} (x) - 2 lo g_{2} (x)

Add similar elements:

3 lo g_{2} (x) - 2 lo g_{2} (x) = lo g_{2} (x)

= lo g_{2} (x)

lo g_{2} (\frac{2 x + 1}{x - 5})

5 lo g_{10} (8) + 2 lo g_{10} (x)

lo g_{6} (\frac{x y}{z t})

\frac{1}{3} ln (a^{2} b^{4})

lo g_{10} (0.5) + lo g_{10} (98)

What is log_{2}(x^3)-log_{2}(x^2) ?
The solution to log_{2}(x^3)-log_{2}(x^2) is log_{2}(x)