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

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

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expand log_{10}((x^3)/2)

expand

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

5 ln (2) + 2 ln (3) - 3 ln (4)

ln (- e i)

- \frac{1}{2} ln (3)

lo g_{4} (\frac{x}{16})

lo g_{7} (x y)

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