if x^(x^2) = 100000 then x will lie between

M4maths Previous Puzzles

22 Mar 2012 power x square x

if x^(x^2) = 100000
then x will lie between

OPtion

1) 1 and 2
2) 2 and 3
3) 3 and 4
4) 4 and 5
5) 5 and 6
6) 8 and 9
7) 10 and 11
8) 16 and 17
9) 20 and 21
10) 100 and 101

Solution

check 3^9 and 4^16

Correct Option: 3 Best Solution (15)

Vignesh   12 years AGO

x^(x^2) = 100000

1^(1^2) = 1^1 ->Below 100000
2^(2^2) = 2^4 ->Below 100000
3^(3^2) = 3^9 ->Below 100000
4^(4^2) = 4^16 ->Exceeds 100000

So, x lie between 3 and 4

Like? Yes (7) | No   

Ashish Pandey   12 years AGO

x^(x^2)=100000
Taking log both sides with base 10.
log(x^(x^2))=log(10^5)
=>(x^2)log(x)=5
Now, putting x=1,
L.H.S.=0
putting x=2,
L.H.S.=1.2041
putting x=3,
L.H.S.=4.2940
putting x=4,
L.H.S.=9.6329
clearly, X lies between 3 and 4.
put

Like? Yes (3) | No   

Bharat Kul Ratan   12 years AGO

3^9=19683 and 4^16=4294967296
hence, value of x will lie between 3 and 4

Like? Yes (3) | No (1)  

dhiresh   12 years AGO

Option 3 is right
because 3^(3^2) less than 100000 and 4^(4^2) is greater than 100000.

Like? Yes (1) | No   

Shiv Kumar   12 years AGO

When X = 3
x^(x^2) = 3^9 = 19683
When x is 4, 4^16 > 100000.
So the X value will be betwee 3 and 4.

Like? Yes (1) | No   

sivakumar   12 years AGO

3^9= 19683

4^16= 4294967296.
X WILL LIE BETWEEN 3 AND 4;

Like? Yes (1) | No   

Akshansh Jain   12 years AGO

Just hit values of x starting from 1

Like? Yes (1) | No   

Rakesh Kumar Kohli   12 years AGO

As 3^9 < 100000 < 4^16
So x lies between 3 and 4

Like? Yes (1) | No   

Balakrishnan M   12 years AGO

if x=2 then 2^(2^2) = 2^4=16,
if x=3 then 3^(3^2) = 3^9=19683100000
then x will lie between 3 and 4

then x will lie between
then x will lie between

Like? Yes (1) | No   

sai ghanasyam   12 years AGO

3^9=19683 and 4^16=4294967296.therefore x lies between 3 and 4.

Like? Yes (1) | No   

chiru   12 years AGO

for x=3 the value of x^(x^2)=19683 and x=3.5 the x^(x^2)=4622038.34(>100000) hence option3 is the reasonable one..

Like? Yes (1) | No   

Mullaji Zubair Dawood   12 years AGO

on solving (x^(x^2))=100000,
The Value we Get is '3.1622776602' Which is Between 3 &4,so Answer 3.!

Like? Yes (1) | No   

Anish Philip   12 years AGO

x^2 log x = 5

Like? Yes (1) | No   

Suresh K   12 years AGO

(x^2)log(x) = 5;
(3 ^2) log 3 = 4.29
(4 ^2) log 4 = 9.63

thus range will be 3 to 4

Like? Yes (1) | No   

Viru Sihag   12 years AGO

3^9=19683
and 4^16=4294967296 that is greater then 100000.
so the value of x lies between 3 and 4.

Like? Yes (1) | No (1)