Question

Solve 7+42· 3²⁻³ᵃ=14· 3⁻²ᵃ+7
a. a=-3
b. a=0
c. a=3
d. no solution

Answer 1

The equation 7 + 42 · 3²⁻³ᵃ = 14 · 3⁻²ᵃ + 7 simplifies to 42 · 3⁻³ᵃ = 14 · 3⁻²ᵃ when the 7 on both sides is canceled out. After solving for 'a', it is determined that the correct value is a = 3.Option C is the correct answer.

Step-by-step explanation:

Solving the equation 7 + 42 · 3²⁻³ᵃ = 14 · 3⁻²ᵃ + 7 involves first simplifying both sides of the equation and then isolating the variable 'a'. Let's break it down:

1. Simplify the exponents on both sides of the equation.
2. Combine like terms.
3. Isolate 'a' to solve for its value.

When simplified, the equation becomes 7 + 42 · 3⁻³ᵃ = 14 · 3⁻²ᵃ + 7. This implies that 42 · 3⁻³ᵃ = 14 · 3⁻²ᵃ, as the 7 on both sides cancel out. By further simplification and solving for 'a', we will be able to determine the correct value that satisfies the equation.

After simplifying, we find that the correct answer is a = 3.