Question

question 1 (mandatory) (1 point) if 3^{x^{2}+1}=243, then x is equal to a) 2 b) 4 or -4 c) 2 or -2 d) 5 or 0

Explanation:

Step1: Rewrite 243 as power of 3

Since \(243 = 3^5\), the equation \(3^{x^{2}+1}=243\) becomes \(3^{x^{2}+1}=3^5\).

Step2: Equate exponents

If \(a^m=a^n\), then \(m = n\). So \(x^{2}+1 = 5\).

Step3: Solve for \(x^{2}\)

Subtract 1 from both sides: \(x^{2}=5 - 1=4\).

Step4: Solve for \(x\)

Taking the square - root of both sides, we get \(x=\pm\sqrt{4}=\pm2\).

Answer:

c) 2 or -2