Question 466404
<font face="Times New Roman" size="+2">

The sum of the logs is the log of the product.

Unspecified base implies base 10

Definition of the logarithm function.

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = \log_b(x) \ \ \Rightarrow\ \ b^y = x]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(1\ +\ x)\ +\ \log(2\ +\ x)\ =\ 2]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left((1\ +\ x)(2\ +\ x)\right)\ =\ 2]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left(2\ +\ 3x\ +\ x^2\right)\ =\ 2]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\ +\ 3x\ +\ x^2\ =\ 10^2\ =\ 100]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 3x\ -\ 98\ =\ 0]

Not factorable.  Use the quadratic formula to solve.  Note: The discriminant is prime.  Exclude the negative root because anything less than -1 is excluded from the domain of your most restrictive log argument, i.e., (1 + x).

Use a calculator to check your work using numerical methods.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>