SOLUTION: Solve for x: {{{e^(3x+1)=1/(e^x-2)}}}

Question 130650: Solve for x:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

Break up to get

Break up to get

Flip the fraction on the right side

Rewrite to get

Now let

Plug in

Multiply both sides by

Multiply

Divide both sides by

Reduce

Now plug in

Multiply

Rewrite as

Since the bases are equal, the exponents are equal

So

Divide both sides by 4 to isolate x

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

Answer:

So our solution is

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