log'base 2' x + 4log 'base x' 2 =5 use the change of base rule
logx / log 2 + 4(log 2)/logx = 5 get a common denominator and simplify
(logx)^2 + 4(log2)^2 = 5log2logx rearrange
(logx)^2 - 5log2logx + 4(log2)^2 = 0 factor
(log x - 4log2)(logx -log2) = 0 set each factor to 0
logx = 4log2 or logx = log2
x = 104log2 or x = 2
log'base 2' x + 4log 'base x' 2 =5 use the change of base rule
logx / log 2 + 4(log 2)/logx = 5 get a common denominator and simplify
(logx)^2 + 4(log2)^2 = 5log2logx rearrange
(logx)^2 - 5log2logx + 4(log2)^2 = 0 factor
(log x - 4log2)(logx -log2) = 0 set each factor to 0
logx = 4log2 or logx = log2
x = 104log2 or x = 2