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solve:

log'base 2' x + 4log 'base x' 2 =5 

thanks

 Nov 27, 2014

Best Answer 

 #1
avatar+128089 
+5

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

 

 Nov 27, 2014
 #1
avatar+128089 
+5
Best Answer

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

 

CPhill Nov 27, 2014

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