Question

Question
Esmeralda wants to solve for x in the equation 3−2x+1⋅3−2x−3=3−3
. Which of the following answers should she select?(1 point)
Responses

x=14

x is equal to 1 fourth

x=−5±73√8

x equals Start Fraction negative 5 plus minus Start Root 73 End Root over 8 End Fraction

x=−4

x equals negative 4

x=−2

Answer 1

Interpret the equation as 3^{−2x+1}·3^{−2x−3}=3^{−3}. Add exponents: 3^{(−2x+1)+(−2x−3)}=3^{−4x−2}=3^{−3}. So −4x−2=−3 → −4x=−1 → x=1/4.

Choose the answer "x is equal to 1 fourth" (x = 1/4).