Question

log4(2*log3(1+log2(1+3*log2(x))))=(1/2)

Answer 1

log₄(2*log₃(1+log₂(1+3*log₂x)))=1/2
2*log₃(1+log₂(1+3*log₂x))=4¹/²
2*log₃(1+log₂(1+3*log₂x))=2
log₃(1+log₂(1+3*log₂x))=1
1+log₂(1+3log₂x)=3¹
log₂(1+3log₂x)=2
1+3log₂x=2²
3log₂x=3
log₂x=1
x=2