Home
Class 12
MATHS
The value of 6+ log(3//2) (1/(3sqrt2)...

The value of
` 6+ log_(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sqrt2)...))))` is ________.

Text Solution

Verified by Experts

The correct Answer is:
4
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`.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Numerical)|18 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))...cdots))))

The value of 6+log_((3)/(2))((1)/(3sqrt(2))sqrt(4-(1)/(3sqrt(2))sqrt(4-...))

The value of log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo) is

The value of 6+(log)_(3/2)[1/(3sqrt(2)) * sqrt{ (4 - 1/(3sqrt(2))) sqrt(4 - 1/(3sqrt(2))....... } is ...............

(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))

(1)/(sqrt(2)+sqrt(3))-(sqrt(3)+1)/(2+sqrt(3))+(sqrt(2)+1)/(2+2sqrt(2))

Evaluate 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))