What is log_{2}(1/32 p^3q) ?

The solution to log_{2}(1/32 p^3q) is -5+3log_{2}(p)+log_{2}(q)

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simplify log_{2}(1/32 p^3q)

simplify

lo g_{2} (\frac{1}{32} p^{3} q)

- 5 + 3 lo g_{2} (p) + lo g_{2} (q)

Solution steps

lo g_{2} (\frac{1}{32} p^{3} q)

\frac{1}{32} = 2^{- 5}

= lo g_{2} (2^{- 5} p^{3} q)

Apply log rule:

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

lo g_{2} (2^{- 5} p^{3} q) = lo g_{2} (2^{- 5}) + lo g_{2} (p^{3} q)

= lo g_{2} (2^{- 5}) + lo g_{2} (p^{3} q)

Apply log rule:

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

lo g_{2} (2^{- 5}) = - 5

= - 5 + lo g_{2} (p^{3} q)

Simplify

lo g_{2} (p^{3} q) : 3 lo g_{2} (p) + lo g_{2} (q)

= - 5 + (3 lo g_{2} (p) + lo g_{2} (q))

Apply rule:

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

- 5 + (3 lo g_{2} (p) + lo g_{2} (q)) = - 5 + 3 lo g_{2} (p) + lo g_{2} (q)

= - 5 + 3 lo g_{2} (p) + lo g_{2} (q)

6 lo g_{2} (x) - 7 lo g_{2} (y)

3 lo g_{7} (v) + 6 lo g_{7} (w) - \frac{lo g _{7} ( u )}{3}

lo g_{2} (6) - lo g_{2} (25) + lo g_{2} (20)

lo g_{10} (x + 1) - lo g_{10} (x)

ln (\frac{e}{5})

What is log_{2}(1/32 p^3q) ?
The solution to log_{2}(1/32 p^3q) is -5+3log_{2}(p)+log_{2}(q)