Work out the value of n 1/3 √ 32 = 2^n

By the way, it should actually be:

work ou the value of n if:

1/3 / √ 32 = 2^n

1/3 √ 32 = 2^n

Hello Guest!

$\frac{1}{3}\cdot \sqrt{2^5}=2^n\\ \sqrt{2^5}=3\cdot 2^n\\ 2^{\frac{5}{2}-n}=3$

$ln2\cdot ({\frac{5}{2}-n})=ln3$

$\frac{5}{2}-n=\frac{ln3}{ln2}$

$n=\frac{5}{2}-\frac{ln3}{ln2}$

$n=0.15037$

  !

OK, why not like this:  1/3 / √ 32 = 2^n

Hello guest from answer  #1!

$\color{BrickRed}\frac{1}{3\cdot \sqrt{32}}=2^n\\ 3\cdot \sqrt{32}=2^{-n}\\ 3\cdot 2^{2.5}=2^{-n}\\ 3=\frac{2^{-n}}{2^{2.5}}\\ 3=2^{-n-2.5}$

$\frac{ln3}{ln2}=-n-2.5$

$n=-2.5-\frac{ln3}{ln2}$

$n=-4.08496$

  !