Find the value of x, x^x^2=16 Olympiad Mathematics

#olympiad

[bandarusatyanandachary]

16 can be written as 2^4
Again 4 can be written as 2^2
Therefore 16 can be written as2^2^2
Therefore x^x^2 = 2^2^2
Therefore x = 2

[jim]

If a^a = b^b, then bases a and b are equal. Look for that format. 16 = 4^2. Square both sides. We have 4^4 on the RHS. Halfway to the format. KEY: the exponent 2 on the LHS goes on the x DOWNSTAIRS for x^2^x^2. So x^2^x^2 = 4^4 and we have the format we want. x^2 = 4 so x = 2.

[bernardweerasinghe]

X^x^2 =16
Taking the square root in both sides:
X^x =+/- 4=+/- 2^2
Thus x=+/-2

[loner_wolf]

X^x ^2 = 16
Let x^x = m
Now
m^2 =16
m^2 = 4^2
now
m = 4
Remember
m = x^x
Now
x^x = 4
X^x= 2^2
Therefore
That what soln I know.

[mishrasir]

We can write x^x^2=2^2^2
Compairing both side
x^x=2^2
Therefore x=2

[weather-streets]

Nice job sir but is that necessary to solve every algebraic equation through general rule rather than uncovering its "subject x", by error and trial method?

[uthmandeniz]

This was a very basic one. We could have assumed x=2 but the method is very important.

[jamesodongo]

Well done master but you're making everything very long and someone else may find it very difficult to understand.

[issackshayo]

Why did you factor 8? You could use law of indices to finish very easily this question as it was base 4 power 2 power 2. Long procedure to students

[manumathai]

Why this round the nose way.

Take square root on both sides you get
x^x = 4
x^x = 2^2
And x=2

[williamedonacien]

Pose: x^x = Y

Y^2 = 16
Y= 4 ou -4

x^x = Y.
==> Y=4 ✅ Y=-4 ❌
x^x = 2^2.

==> x=2

[Greebstreebling]

I never did find out why integrating 1+ Tan squared (x) was any use to me in life....

[lorenzogcapra]

Depending on the associativity of expone ntiation op you may interpreti as (x^x)^2
In that case, the only solution is x=2

[yatenzer]

You went from Mumbai to New Delhi via Madurai - did opposite operation and then solved more complicated problem

[ysy]

Bruh, I just inserted both 2 and -2, because I immediately spotted the solution.

[tetrahedron]

2 to the power of 4 is 16. 2 to the power of 2 is 4. Therefore, the answer is 2.

[baselinesweb]

Why don't you just write 16 as (2^2)^2, then it is immediately clear what x is.

[RizwanKhan-ibxh]

16 can be 2^2^2 . So the answer is 2 on comparing.

[arnoldmalalay]

Maybe you can apply logarithm function.it so easy to solve...

[suindude]

By taking log both sides...2logx logx=2log4so xis 2