What is log_{2}(1/2 mn^3) ?

The solution to log_{2}(1/2 mn^3) is -1+log_{2}(m)+3log_{2}(n)

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simplify log_{2}(1/2 mn^3)

simplify

lo g_{2} (\frac{1}{2} m n^{3})

- 1 + lo g_{2} (m) + 3 lo g_{2} (n)

Solution steps

lo g_{2} (\frac{1}{2} m n^{3})

\frac{1}{2} = 2^{- 1}

= lo g_{2} (2^{- 1} m n^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (2^{- 1} m n^{3}) = lo g_{2} (2^{- 1}) + lo g_{2} (m n^{3})

= lo g_{2} (2^{- 1}) + lo g_{2} (m n^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{- 1}) = - 1

= - 1 + lo g_{2} (m n^{3})

Simplify

lo g_{2} (m n^{3}) : lo g_{2} (m) + 3 lo g_{2} (n)

= - 1 + (lo g_{2} (m) + 3 lo g_{2} (n))

Apply rule:

a + (b + c) = a + b + c

- 1 + (lo g_{2} (m) + 3 lo g_{2} (n)) = - 1 + lo g_{2} (m) + 3 lo g_{2} (n)

= - 1 + lo g_{2} (m) + 3 lo g_{2} (n)

lo g_{10} (x) + lo g_{10} (x - 9)

2 lo g_{10} (3) + lo g_{10} (8)

2 lo g_{10} (3) + lo g_{10} (5)

lo g_{10} (p) - 3 lo g_{10} (q) - \frac{1}{2} lo g_{10} (n)

lo g_{10} \frac{m}{( \frac{p}{q} )}

What is log_{2}(1/2 mn^3) ?
The solution to log_{2}(1/2 mn^3) is -1+log_{2}(m)+3log_{2}(n)