A log question.

log(x) 8 + log (8) X =4
(log8)/logx + (logx)/log8 = 4
(log8)^2 + (logx)^2 = 4(log8)(logx)
(logx)^2 - 4(log8) (logx) + (log8)^2 = 0
logx = { 4log8 +/- √[(4log8)^2 - 4(log8)^2] } / 2
logx = [ 4log8 +/- √12(log8)^2] / 2
logx = 2log8 +/- (√3)(log8)
logx = (2 + √3)log8 or (2 - √3)log8
logx = log ( 8 ^ (2 + √3) ) or log ( 8 ^ (2 - √3) )
x = 8 ^ (2 + √3) or 8 ^ (2 - √3)

log(x) 8 + log (8) X =4

log 8 / log x + log x / log 8 = 4

(log 8)^2 + (log x)^2 = 4 log 8 log x

(log x)^2 - 4 log 8 log x + (log 8)^2 = 0

log x = {4 log 8 + √[(4log 8)^2 - 4(1)(log8^2)]} / 2
= [4 log 8 + √12 (log8)]/2
= 2 log 8 + √3 log 8
= (2 + √3) log 8
x = 8^(2 + √3)

or

log x = {4 log 8 - √[(4log 8)^2 - 4(1)(log8^2)]} / 2
= [4 log 8 - √12 (log8)]/2
= 2 log 8 - √3 log 8
= (2 - √3) log 8
x = 8^(2 - √3)