The value of `6+(log)_(3//2)(1/(3sqrt(2))sqrt(sqrt(4-1/(3sqrt(2)))sqrt(4-1/(sqrt(2)))sqrt(4-1/(3sqrt(2)))))` is ...............

Answer

4

Explanation

Let ` sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)...)))= y`
So, ` 4-1/(3sqrt2)y=y^(2)" "(y gt 0)`
` or y^(2)+1/(3sqrt2)y-4 = 0`
` or y = 8/(3sqrt2)`
So, the required value is
` 6+log_(3//2)(1/(3sqrt2)xx8/(3sqrt2))=6 + log_(3/2). 4/9= 6 - 2 = 4`.