Question

homework3: problem 5 (2 points) solve the exponential equation. 3^{x^{2}-3x}=3^{-2} has two solutions x_1,x_2 = note enter your answer as a comma separated list. you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Use exponential - property

If \(a^m=a^n\), then \(m = n\) for \(a>0,a
eq1\). Here \(a = 3\), so \(x^{2}-3x=-2\).

Step2: Rearrange to quadratic form

Rearrange \(x^{2}-3x=-2\) to \(x^{2}-3x + 2=0\).

Step3: Factor the quadratic

Factor \(x^{2}-3x + 2\) as \((x - 1)(x - 2)=0\).

Step4: Solve for \(x\)

Set each factor equal to zero: \(x-1 = 0\) gives \(x=1\); \(x - 2=0\) gives \(x=2\).

Answer:

1,2