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)
1.) x=1/4
2.) x= -4
3.) x= -5±73√/8
4.) x= -2
To solve the equation, Esmeralda can begin by using the property of exponents that states when multiplying two numbers with the same base, the exponents can be added.
So, rewriting the equation with the same base (3), we get:
3^(-2x+1)*3^(-2x-3) = 3^(-3)
Now, she can use another property of exponents that states when dividing two numbers with the same base, the exponents can be subtracted.
So, rewriting the equation with division, we get:
3^(-2x+1-2x-3) = 3^(-3)
Simplifying the exponents, we have:
3^(-4x-2) = 3^(-3)
Since the bases are the same (3) and the exponents are equal, the equation simplifies to:
-4x-2 = -3
Adding 2 to both sides:
-4x = -1
Dividing by -4:
x = 1/4
Therefore, Esmeralda should select answer choice 1.) x = 1/4.