math
posted by Katie .
6^(2log(x)) = 8

assuming logs base 10,
2logx = log_6(8)
logx = 1/2 log_6(8)
x = √(10^(log_6(8))
now log_6(8) = log6/log8. so
x = √(10^log6)^(1/log8)
= √(6^1/log8)
= 6^(1/log64) 
take log of both sides
log [ 6^(2logx) ] = log8
2logx (log6) = log8
2logx = log8/log6
log x^2= log8/log6
x^2= 10^(log8/log6)
x = √( 10^(log8/log6) ) = 3.804339012
check using your calculator, it works 
Go with Reiny's answer. I messed up my log base conversion.