SOLUTION: Solve for x (nearest 10th) 3^ x square root 2 + 4. 3^ x square root 8 -3 =0

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Question 271636: Solve for x (nearest 10th)
3^ x square root 2 + 4. 3^ x square root 8 -3 =0

Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!













Let some letter other than , say ,

equal to . 

Then we have .  Substituting,



Factoring:





Use the zero factor principle.

Set the first factor = 0





Setting second factor = 0




Using first solution for  in

,



Take logs of both sides

 

Use rules of logarithms:



Divide both sides by 

 

Get a calculator and punch out the left side:



That's one solution.  We must also consider 

the solution for t  to see if that 

also yields a solution for x:

Using this solution for  in

.

.

No power of 3 can ever be negative, so we discard
the solution for ,  as extraneous.

The only solution is  

, rounded to tenths is t=-.2

Edwin

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