What is expand log_{2}((4uv^3)^2) ?

The solution to expand log_{2}((4uv^3)^2) is 4+2log_{2}(u)+6log_{2}(v)

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expand log_{2}((4uv^3)^2)

expand

lo g_{2} ((4 u v^{3})^{2})

4 + 2 lo g_{2} (u) + 6 lo g_{2} (v)

Solution steps

lo g_{2} ((4 u v^{3})^{2})

Apply log rule:

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

lo g_{2} ((4 u v^{3})^{2}) = 2 lo g_{2} (4 u v^{3})

= 2 lo g_{2} (4 u v^{3})

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 lo g_{2} (4) + 2 lo g_{2} (u) + 2 \cdot 3 lo g_{2} (v)

Multiply the numbers:

2 \cdot 3 = 6

= 2 lo g_{2} (4) + 2 lo g_{2} (u) + 6 lo g_{2} (v)

2 lo g_{2} (4) = 4

= 4 + 2 lo g_{2} (u) + 6 lo g_{2} (v)

lo g_{e} (\frac{4}{3})

2 lo g_{2} (y - 6) - 4 lo g_{2} (y + 7)

ln (3 ab \cdot 2 c)

\frac{5}{2} (ln (5) - ln (2))

ln (\frac{2 ^{- 3}}{3 ^{2} 5 ^{2}})

What is expand log_{2}((4uv^3)^2) ?
The solution to expand log_{2}((4uv^3)^2) is 4+2log_{2}(u)+6log_{2}(v)