Question

Order the equations from least to greatest based on the number of solutions to each equation.

a. (-3x + 6 = 2^x + 13^(-3))
b. (2^x - 2 - 4^x - 1 = 3^(-x) - 2)
c. (13^(-3) = 2^x - 2)

Answer 1

To order the equations from least to greatest based on the number of solutions, we need to determine the number of solutions for each equation. The order is c, a, b.

Step-by-step explanation:

To order the equations from least to greatest based on the number of solutions, we need to determine the number of solutions for each equation.

Starting with equation b, we can simplify it to 2^x - 2 - 4^(x-1) = 3^(-x) - 2. This equation has two terms on either side and can be rewritten as a quadratic equation. We can solve this equation and find the number of solutions.

Moving on to equation c, we have 13^(-3) = 2^x - 2. This equation has a single term on either side, and we can solve it to find the number of solutions.

Lastly, equation a can also be simplified and rewritten as a quadratic equation. We can solve it to determine the number of solutions.

Therefore, the order from least to greatest based on the number of solutions is c, a, b.