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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

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

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

4 [ln (z) + ln (z + 5)] - 2 ln (z - 5)

ln (x^{2} y)

lo g_{5} (\frac{14 x}{y})

lo g_{4} (\frac{( 2 x + 1 )}{3 y + 4})

lo g_{10} (y) + 13 lo g_{10} (z)

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