What is expand log_{2}((4x^3)/(x^2-3x-18)) ?

The solution to expand log_{2}((4x^3)/(x^2-3x-18)) is 2+3log_{2}(x)-log_{2}(x^2-3x-18)

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expand log_{2}((4x^3)/(x^2-3x-18))

expand

lo g_{2} (\frac{4 x ^{3}}{x ^{2} - 3 x - 18})

2 + 3 lo g_{2} (x) - lo g_{2} (x^{2} - 3 x - 18)

Solution steps

lo g_{2} (\frac{4 x ^{3}}{x ^{2} - 3 x - 18})

Apply log rule:

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

lo g_{2} (\frac{4 x ^{3}}{x ^{2} - 3 x - 18}) = lo g_{2} (4 x^{3}) - lo g_{2} (x^{2} - 3 x - 18)

= lo g_{2} (4 x^{3}) - lo g_{2} (x^{2} - 3 x - 18)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{2} (4 x^{3}) = lo g_{2} (4) + lo g_{2} (x^{3})

= lo g_{2} (4) + lo g_{2} (x^{3}) - lo g_{2} (x^{2} - 3 x - 18)

Apply log rule:

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

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

= lo g_{2} (4) + 3 lo g_{2} (x) - lo g_{2} (x^{2} - 3 x - 18)

lo g_{2} (4) = 2

= 2 + 3 lo g_{2} (x) - lo g_{2} (x^{2} - 3 x - 18)

ln (6) + ln (\frac{e ^{(2.48199)}}{3})

(ln (100) - ln (95)) \cdot 100

lo g_{5} (x - 2) + lo g_{5} (x - 6)

ln (\frac{y}{2 b ^{2}})

What is expand log_{2}((4x^3)/(x^2-3x-18)) ?
The solution to expand log_{2}((4x^3)/(x^2-3x-18)) is 2+3log_{2}(x)-log_{2}(x^2-3x-18)