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.Com
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) (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.
\ =\ \ln\left(5^{\small x\,-\,2}\right))
Use \ =\ n\log_b(x))
to write:
\ =\ (x\ -\ 2)\,\ln(5))
Then keeping in mind that )
and )
are nothing more than irrational numerical constants, we play a little algebra music:
\ =\ x\ln(5)\ -\ 2\ln(5))
\ -\ x\ln(5)\ =\ -2\ln(5))
\ -\ \ln(5)\right)\ =\ -2\ln(5))
}{\left(2\ln(3)\ -\ \ln(5)\right)})
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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