Question

homework3: problem 4 (2 points) results for this submission the answer is not correct. solve the exponential equation. 2^{x^{2}-2x}=2^{8} has two solutions x_1,x_2 = note enter your answer as a comma separated list. preview my answers submit answers your score was recorded. you have attempted this problem 2 times. you received a score of 0% for this attempt. your overall recorded score is 0%. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Use exponential - property

If \(a^m=a^n\), then \(m = n\) for \(a>0,a
eq1\). Given \(2^{x^{2}-2x}=2^{8}\), we have \(x^{2}-2x = 8\).

Step2: Rearrange to quadratic - form

Rearrange \(x^{2}-2x = 8\) to \(x^{2}-2x - 8=0\).

Step3: Factor the quadratic

Factor \(x^{2}-2x - 8\) as \((x - 4)(x+2)=0\).

Step4: Solve for \(x\)

Set each factor equal to zero: \(x - 4=0\) gives \(x = 4\); \(x + 2=0\) gives \(x=-2\).

Answer:

\(4,-2\)