SOLUTION: find the value of x in this equation : log(x+3)+log(x-1)=0

Question 578477: find the value of x in this equation :
log(x+3)+log(x-1)=0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Logarithm of a product is the sum of the logarithms of the factors, so
-->
The next step is the transformation
-->
achieved applying antilogarithm (inverse function of logarithm, ) to both sides
or
From then on, it's a quadratic equation
--> -->
Here we apply the quadratic formula.

The positive solution, , makes both factors positive:
and
and exist, and
is a valid solution of the original equation.
The negative solution, , is an extraneous solution.
It makes both factors negative:
and , and as a consequence
and do not exist for that x value, so it is not a solution of the original equation.

RELATED QUESTIONS
Find the value of x. ln (x-3)-2=0 Solve the logarithmic equation. log x +... (answered by stanbon)

Find the solution(s) of the equation?... (answered by user_dude2008)

find the solution(s) of the equation?... (answered by Earlsdon)

What is the value of x log(base 3)x-log(base... (answered by lwsshak3)

Please help me solve this equation if log(x^3+3)base 10 - log(x+7)base 10 + log2base10=... (answered by MathLover1,MathTherapy,ikleyn)

Find the positive value of x that satisfies the equation Logx-log( x + 6)^1/2 = 0 All... (answered by MathLover1,Alan3354)

find the approximate value of x in the following equation: 2 log x = log... (answered by robertb)

find the value of x in the following equation: 2 log x = log... (answered by stanbon)

the value of x in the following equation: 3 log x = log 125 is it... (answered by Nate)