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Can I please get help in solving this equation. Thanks :)
e^2x - 5e^x + 6 = 0
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It is 129-th time as we, the tutors, ask you DO NOT USE words "solve question". There is no such term in English.
Simply say "solve equation". T h a n k s.
Standard way is introducing new variable y = .
Then the equation takes the form
y^2 - 5x + 6 = 0.
Factor left side:
(y-2)*(y-3) = 0.
There are 2 solutions: y = 2 and y = 3.
1) y = 2 ====> = 2 ====> x = ln(2).
2) y = 3 ====> = 3 ====> x = ln(3).
Answer. There are two solutions: x = ln(2) and x = ln(3).
Check. 1) x = ln(2): = = = 4 - 10 + 6 = 0. ! Correct !
2) x = ln(3): = = = 9 - 15 + 6 = 0. ! Correct !
Solved.