What is log_{10}(x^3)-log_{10}(x^2) ?

The solution to log_{10}(x^3)-log_{10}(x^2) is log_{10}(x)

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simplify log_{10}(x^3)-log_{10}(x^2)

simplify

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

lo g_{10} (x)

Solution steps

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

Apply log rule

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

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

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

Apply log rule

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

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

= 3 lo g_{10} (x) - 2 lo g_{10} (x)

Add similar elements:

3 lo g_{10} (x) - 2 lo g_{10} (x) = lo g_{10} (x)

= lo g_{10} (x)

lo g_{e} (\frac{17}{4})

5 lo g_{b} (x) - lo g_{b} (y) + \frac{1}{4} lo g_{b} (z)

lo g_{2} (6) - \frac{1}{2} lo g_{2} (3)

5 ln (x^{3}) - \frac{1}{3} ln (7 - x^{3})

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

What is log_{10}(x^3)-log_{10}(x^2) ?
The solution to log_{10}(x^3)-log_{10}(x^2) is log_{10}(x)