• Placement Papers
• /
• Elitmus
• /
• Category

Elitmus Question Papers:

(#M40040068) ELITMUS Category question Keep an EYE

log(e(e(e...)^1/3)^1/3)^1/3 what will be its value?

Asked In Elitmus Jayesh Hazari (10 years ago)

Solved subodh khandelwal Read Solution (3)

Is this Puzzle helpful?   (9)   (5) Submit Your Solution

Read Solution (3) :

subodh khandelwal  (10 years ago) Best Solution

let us assume [log(e(e(e..)^1/3)^1/3)^1/3] = x
now as log m^n = n log(m)
we can write it as 1/3[log(e(e(e...)^1/3)^1/3)] = x
now 1/3[log(e)+log(e(e..)^1/3)^1/3)] = x
now we can see that it is again our question so we can replace it as x
so 1/3(1+x)= x
=> 3x = 1+x
=> x= 1/2

Is this solution Helpfull? Yes (21) | No (4)  

DINKAR BHARTI  (10 years ago)

e(e(e..)^1/3)^1/3)^1/3=e^(1/3+1/9++1/27+......infinte series)=e^(1/3)/(1-1/3)=e^1/2
now,
loge^1/2=1/2loge=1/2*1=1/2 since loge base e=1

Is this solution Helpfull? Yes (13) | No   

Ashutosh Ranjan  (10 years ago)

Let x=(e(e(e.........)^1/3)^1/3)^1/3)
now squaring both side we get
x^3=e(e(e(e.........)^1/3)^1/3)^1/3)
i.e., x^3=e*x [since x=(e(e(e.........)^1/3)^1/3)^1/3)]
therefore x=e [since x can not be zero]
Finally, log(x)=log(e^1/2)=1/2

Is this solution Helpfull? Yes (3) | No   

Please Login to Read Solution.