solve the equation

Question

Log²(4-x)+log(4-x)log(x+1/2)-log²(x+1/2)=0

Answer 1

I think that you have copied the question wrong.. 

if it has to be an easier question then [ log (x+1/2)]^2should be multiplied by 2.

 

I will do the question with that assumption.

 

let log (4-x) be a and log(x+1/2)be   b

 then the question is a^2 +ab- 2b^2=0

 

which can be factorised as( a-2b) (a+b)=0

 

so either a=2b or a= -b

 

a=2b will give log (4-x)= 2 log (x+1/2)

 

ie 4-x = (x+1/2)^2    make it a quadratic in x and solve for x...

similarly 

 

a=-b gives log(4-x)= -log(x+1/2)

 

 

ie 4-x= 1/(x+1/2)  this will again give a quadratic in x which you can solve...

dont forget to check whether the values of x that you get  are satifying the original equation or not  

 

 

 

enjoy:)