Exponential equations
Answers are for parents and teachers.
1
Solve 5^(2x−1) = 125.
2
2
Solve (1/3)^(x−2) = 9.
3^(2−x) = 3² ⇒ 2 − x = 2 ⇒ x = 0.
3
Solve 3^(x+2) + 3ˣ = 270.
3ˣ · (9 + 1) = 270 ⇒ 3ˣ = 27 ⇒ x = 3.
4
Solve 25ˣ − 6 · 5ˣ + 5 = 0.
t = 5ˣ: t² − 6t + 5 = 0, t = 1 or 5 ⇒ x = 0 or x = 1.
5
Solve the system 3ˣ · 3ʸ = 81, x − y = 2.
x + y = 4 and x − y = 2 ⇒ x = 3, y = 1.