How do I do this logarithm by hand. log2(log3(y))=3?

Question

please show all steps to solving it plz

Answer 1

log2(log3(y))=3

let x=log3(y) so question becomes log2(x)=3

convert to indices -> 2^3=x which is 2^3=log3(y)

log3(y)=8 --> y=3^8

get it?

Answer 2

you put to exponential
remember that y= a^x means x = log base a of y
so log2(log3(y)) =3 equivalent to (

log3(y) = 2^3 = 8

and y = 3^8 =6561

Answer 3

log2(log3(y))=3
thus y={10^ [ (10^3) / 2 ] } /3=(10^500)/3
this can be solved mentally.
assuming log is base 10.
if 2 and 3 are the bases then it get's easier...
y=3^(2^3)=3^8=81*81=6561..