Log3(X-1)+log3(X+3)-log(x+1)=1 find solution?

Question

elaborate the solution of above problem.

Answer 1

Consider the equation as .

Apply Product property of natural logarithm : .

Apply quotient  property of natural logarithm : .

Apply exponential property of natural logarithm : .

 

.

Factor by grouping.

Factor :

Apply zero product property.

.

Therefore, the solution of the given equation is .

Comments

We cannot have a log of a negative number, so x= - 2 must be rejected.

So, the solution is x = 3.