8
AssignmentMultiple Choice

Solving Exponential Equations by Rewriting the Base

Question 8 • PBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024

Solve:363s = 2162s+1

Answer
A
s = –3
B
s = 1
C
s = 3
D
no solution

Explanation

Rewrite both bases as powers of 6: 36 = 6² and 216 = 6³. Then the equation becomes 6^(6s) = 6^(6s+3). Since the bases are equal and greater than 1, the exponents would have to be equal, but that would require 6s = 6s + 3, which is impossible. So the equation has no solution.

AI-written and checked against the verified answer.

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