Final answer:
To find the extraneous solution to the logarithmic equation 2 log(x + 1) = 2, solve the equation and check if any values make the equation undefined. None of the given options show an extraneous solution.
Step-by-step explanation:
To find the extraneous solution to the logarithmic equation 2 log(x + 1) = 2, we need to solve the equation and check if any values make the equation undefined. First, we can simplify the equation by dividing both sides by 2 to get log(x + 1) = 1. We can rewrite this equation in exponential form, which gives us 10^1 = x + 1. Solving for x, we get x = 9. However, we need to check if x = 9 is an extraneous solution by substituting it back into the original equation. We find that 2 log(9 + 1) = 2 log(10) = 2, which means x = 9 is not an extraneous solution. Therefore, none of the given options shows an extraneous solution.
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