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log5x+log(x-1)=2

 May 21, 2015

Best Answer 

 #1
avatar+129270 
+5

log5x+log(x-1)= 2         Note.......   2 = log 100

 

log (5x * (x -1) )  =  log 100        and we can now just  ignore the logs and solve directly

 

5x ( x - 1)   = 100    simplify

 

5x^2 - 5x   = 100   

 

5x^2  - 5x  - 100  = 0      divide through by 5

 

x^2 - x - 20   = 0       factor

 

(x - 5) ( x + 4)  = 0        and setting both factors to 0 we have that  x = 5 or x  = -4

 

We must reject -4   because it makes the original logs negative......and that's undefined.....thus......

 

x = 5  is the solution

 

 

 May 21, 2015
 #1
avatar+129270 
+5
Best Answer

log5x+log(x-1)= 2         Note.......   2 = log 100

 

log (5x * (x -1) )  =  log 100        and we can now just  ignore the logs and solve directly

 

5x ( x - 1)   = 100    simplify

 

5x^2 - 5x   = 100   

 

5x^2  - 5x  - 100  = 0      divide through by 5

 

x^2 - x - 20   = 0       factor

 

(x - 5) ( x + 4)  = 0        and setting both factors to 0 we have that  x = 5 or x  = -4

 

We must reject -4   because it makes the original logs negative......and that's undefined.....thus......

 

x = 5  is the solution

 

 

CPhill May 21, 2015

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