SOLUTION: 3^x = the square root of 5^x-2 How would you do this problem? I know you have to get rid of the square root sign but I'm stuck after that.

Algebra ->  Square-cubic-other-roots -> SOLUTION: 3^x = the square root of 5^x-2 How would you do this problem? I know you have to get rid of the square root sign but I'm stuck after that.      Log On


   

Question 730140: 3^x = the square root of 5^x-2
How would you do this problem? I know you have to get rid of the square root sign but I'm stuck after that.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I have to presume you mean because the alternate interpretation, namely , has no real number solutions.

Square both sides:



Take the log of both sides, any base, it really doesn't matter. I'll use the natural log.



Use to write:



Then keeping in mind that and are nothing more than irrational numerical constants, we play a little algebra music:









John

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