Math  /  Algebra

QuestionCheck for extraneous solutions.
8. ln2a=9\ln 2 a=9

2

Studdy Solution
Check for extraneous solutions. Since the natural logarithm function is defined for positive arguments, we need to ensure that 2a>0 2a > 0 . Given a=e92 a = \frac{e^9}{2} , we have:
2a=e9 2a = e^9
Since e9 e^9 is positive, 2a 2a is also positive, confirming that the solution is valid and not extraneous.
The solution for a a is:
e92 \boxed{\frac{e^9}{2}}

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