SOLUTION: Please help me solve this equation if log(x^3+3)base 10 - log(x+7)base 10 + log2base10= log x base10, find the value of x

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Question 1184275: Please help me solve this equation
if log(x^3+3)base 10 - log(x+7)base 10 + log2base10= log x base10, find the value of x
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!





........if log same, we have









....factor

















solutions:







Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Please help me solve this equation
if log(x^3+3)base 10 - log(x+7)base 10 + log2base10= log x base10, find the value of x
It's the NORM to apply base 10 for LOGS without a base, so we have: 

          Since all logs above have the same base, we can say that: 

      With logs having same base on both sides of equation, we get: 
                                                                     -------- Cross-multiplying
Using the RATIONAL ROOT THEOREM, we find 2 of the 3 roots. x = 1, and x = - 2. When long division of polynomials or
SYNTHETIC DIVISION is used, we find the other root to be .
Therefore, 

Thanks to IKLEYN for pointing this out. I failed to notice that one of the solutions is negative and therefore creates 
an EXTRANEOUS solution, Therefore, correct solutions are: .
Thanks, @IKLEYN.
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.

Notice that the value   x= -2   is  NOT  a  SOLUTION  to the given equation.


It is a typical  EXTRANEOUS  solution,  which should be  EXLUDED  from the answer list after final checking,

since it produces negative argument of the logarithm in the very first term of the original equation.



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