What is expand log_{2}((2x)^3(x+1)) ?

The solution to expand log_{2}((2x)^3(x+1)) is 3+3log_{2}(x)+log_{2}(x+1)

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expand log_{2}((2x)^3(x+1))

expand

lo g_{2} ((2 x)^{3} (x + 1))

3 + 3 lo g_{2} (x) + lo g_{2} (x + 1)

Solution steps

lo g_{2} ((2 x)^{3} (x + 1))

Apply log rule:

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

lo g_{2} ((2 x)^{3} (x + 1)) = lo g_{2} ((2 x)^{3}) + lo g_{2} (x + 1)

= lo g_{2} ((2 x)^{3}) + lo g_{2} (x + 1)

Apply log rule:

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

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

= 3 lo g_{2} (2 x) + lo g_{2} (x + 1)

Apply log rule:

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

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

= 3 lo g_{2} (2) + 3 lo g_{2} (x) + lo g_{2} (x + 1)

3 lo g_{2} (2) = 3

= 3 + 3 lo g_{2} (x) + lo g_{2} (x + 1)

lo g_{10} (\frac{8 x ^{7} y ^{3}}{z ^{4}})

ln (3 e^{4})

ln (\frac{s ^{2} + 16}{s ^{2} + 64})

ln (\frac{12}{5})

ln (x) + 2 ln (y) - 3 ln (z)

What is expand log_{2}((2x)^3(x+1)) ?
The solution to expand log_{2}((2x)^3(x+1)) is 3+3log_{2}(x)+log_{2}(x+1)