6
AssignmentMultiple Choice

Solving Exponential Equations by Rewriting the Base

Question 6 • PBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024

Solve: 493x = 3432x+1

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

Explanation

Rewrite the bases as powers of 7: 49 = 7² and 343 = 7³. Then the equation becomes 7^(6x) = 7^(6x+3). Since equal powers of 7 must have equal exponents, this would require 6x = 6x + 3, which is impossible. Therefore, the equation has no solution.

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