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Find the solution interval for the inequality: ln(x^(2)+2) <= 6.2

Find the solution interval for the inequality:\newlineln⁡(x2+2)≤6.2 \ln \left(x^{2}+2\right) \leq 6.2

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Full solution

Q. Find the solution interval for the inequality:\newlineln⁡(x2+2)≤6.2 \ln \left(x^{2}+2\right) \leq 6.2
  1. Isolate x2x^2 term: First, let's isolate the x2x^2 term by getting rid of the natural logarithm.\newlineeln⁡(x2+2)≤e6.2e^{\ln(x^2+2)} \leq e^{6.2}\newlinex2+2≤e6.2x^2 + 2 \leq e^{6.2}
  2. Subtract to solve for x2x^2: Now, we need to subtract 22 from both sides to solve for x2x^2.x2≤e6.2−2x^2 \leq e^{6.2} - 2
  3. Calculate and subtract: Let's calculate e6.2e^{6.2} and then subtract 22. \newlinex2≤e6.2−2x^2 \leq e^{6.2} - 2\newlinex2≤492.749041−2x^2 \leq 492.749041 - 2\newline$x^\(2\) \leq \(490\).\(749041\)

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