What is log_{10}(x^4)-log_{10}(x^3) ?

The solution to log_{10}(x^4)-log_{10}(x^3) is log_{10}(x)

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simplify log_{10}(x^4)-log_{10}(x^3)

simplify

lo g_{10} (x^{4}) - lo g_{10} (x^{3})

lo g_{10} (x)

Solution steps

lo g_{10} (x^{4}) - lo g_{10} (x^{3})

Apply log rule

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= 4 lo g_{10} (x) - lo g_{10} (x^{3})

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)

= 4 lo g_{10} (x) - 3 lo g_{10} (x)

Add similar elements:

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

= lo g_{10} (x)

lo g_{10} (\frac{10 b}{3})

0.5 ln (0.5) - 3 ln (3)

ln (2 \cdot e^{x})

ln (\frac{x x ^{3} - 1}{x ^{5} + 9})

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 5 lo g_{c} (x)

What is log_{10}(x^4)-log_{10}(x^3) ?
The solution to log_{10}(x^4)-log_{10}(x^3) is log_{10}(x)