SOLUTION: Solve the equation & check your answer(s):
ln(2-2x)=ln(x+5)+ln(x+4)
Algebra.Com
Question 454385: Solve the equation & check your answer(s):
ln(2-2x)=ln(x+5)+ln(x+4)
Found 2 solutions by nerdybill, solver91311:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
ln(2-2x)=ln(x+5)+ln(x+4)
ln(2-2x)=ln(x+5)(x+4)
(2-2x)=(x+5)(x+4)
2-2x= x^2 +9x + 20
2 = x^2 + 11x + 20
0 = x^2 + 11x + 18
0 = (x+9)(x+2)
x = {-9,-2}
Testing each of the solution above, we see that -9 is an "extraneous solution" and must be thrown out leaving:
x = -2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \ln(x\ +\ 5)\ +\ \ln(x\ +\ 4))
The sum of the logs is the log of the product:
\ =\ \ln(x^2\ +\ 9x\ +\ 20))
Then
\ =\ \log_b\left(\chi_2\right)\ \Leftrightarrow\ \chi_1\ =\ \chi_2)
Hence
So
Just solve for 
. Exclude any root that would make the argument of any of the original logarithm functions less than or equal to zero.
John
My calculator said it, I believe it, that settles it
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