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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

+ 9 ln (y) + 4 ln (2 x - 1) + 5 ln (x - 1)

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

- \frac{1}{3} (ln (7) - ln (26))

10 lo g_{10} (\frac{2}{1}) + 10 lo g_{10} (\frac{0.007}{1}) + 52

ln (x^{2} y) - ln (y^{2})

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