Which of the following shows the extraneous solution to the logarithmic equation 2 log sub 5 open paren x plus 1 close paren is equal to 2 ?

Divide both sides of 2 log₅(x + 1) = 2 by 2 to get log₅(x + 1) = 1, so x + 1 = 5 and x = 4. The original logarithm requires x + 1 > 0, or x > −1. Thus x = −6 is not allowed and is the extraneous solution; choice B is “x is equal to negative 6.”

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