Can you solve this?

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#maths
#mathematics
#olympiad

[@PradeepKumarJ-d4x]

Good efforts

[@2sljmath]

🙏

[@nasrullahhusnan2289]

Power tower must be executed from top to the bottom.
Let 2^x=u and 3^x=v --> 2^v=3^u
Take log: vlog(2)=ulog(3)
(3^x)log(2)=(2^x)log(3)
Divide by (3^x)log(3):
(⅔)^x=[log(2)]/log(3)
Again take log to get x:
x=log[{log(2)}/log(3)]/[log(2)-log(3)]

[@chinmay_0518]

What is the difference between
2^2^3 and (2^2)^3

[@2sljmath]

2^2^3=2^8=256
(2^2)^3=4^3=64
Or
(2^2)^3=2^(2*3)=2^6=64
🙏

[@srinivasch-re2oq]

Apply logerthms.

[@nasrullahhusnan2289]

Power tower must be executed from top to the bottom.
Let 2^x=u and 3^x=v --> 2^v=3^u
Take log: vlog(2)=ulog(3)
(3^x)log(2)=(2^x)log(3)
Divide by (3^x)log(3):
(⅔)^x=[log(2)]/log(3)
Again take log to get x:
x=log[{log(2)}/log(3)]/[log(2)-log(3)]