Work out the value of n

log (1/4*sqrt2)  =  n log 2

 n =   log (1/4 sqrt2) / log 2 =   - 1.5

or

2^-2   * 2^1/2  = 2 ⁿ      

2^(-2+1/2)       = 2ⁿ     equate the exponents

-1/5 = n