SOLUTION: Using suitable substitutions solve for x, 2e^x=7√e^x -3

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Question 1147557: Using suitable substitutions solve for x, 2e^x=7√e^x -3
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

            Look into your post, please, as it came to the forum.

            From the post, it is UNCLEAR how far the square root symbol is spreading to the right. 


If your equation is   


     =  - 3      (1)


then the solution is as follows.



Introduce new variable  u = .


Then the equation (1) takes the form


     = 7*u - 3

     = 0

    (2u-1)*(u-3) = 0


Case 1.  2u - 1 = 0

                 u = 

                 = 

                 = 

                x =  = -2*ln(2).  

                It is the answer for Case 1.



Case 2.  u - 3 = 0

                 u = 3

                 = 3

                 = 9

                x =  = 2*ln(3).  

                It is the answer for Case 2.


ANSWER.  The given equation has two solutions,  -2*ln(2)  and  2*ln(3).


Solved.

--------------

The solution by @greenestamps has editorial deficiencies,

so I came to fix them.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let

Then the equation is





or

(1)



(2)




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