Solving an Exponential Equation? 3^(x^2 + x) = x^1/2

sylphrena

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Dec 1, 2015
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Problem is 3^(x^2+x)=x^1/2

Hi! I'm having a lot of trouble with this problem. The fact that the first x is squared is making it hard for me to isolate the variable. I've been trying to figure this one out for nearly an hour.

So far...

(x^2+x)ln3=1/2lnx
(ln3)x^2+xln3=1/2lnx

All right. Normally I'd want to place terms involving x to one side. But how do I go about doing this now when everything has x and there is that pesky x^2?
 
Problem is 3^(x^2+x)=x^1/2

Hi! I'm having a lot of trouble with this problem. The fact that the first x is squared is making it hard for me to isolate the variable. I've been trying to figure this one out for nearly an hour.

So far...

(x^2+x)ln3=1/2lnx
(ln3)x^2+xln3=1/2lnx

All right. Normally I'd want to place terms involving x to one side. But how do I go about doing this now when everything has x and there is that pesky x^2?

That equation does not have any solution in real domain.
 
Problem is 3^(x^2+x)=x^1/2

Hi! I'm having a lot of trouble with this problem. The fact that the first x is squared is making it hard for me to isolate the variable. I've been trying to figure this one out for nearly an hour.

So far...

(x^2+x)ln3=1/2lnx
(ln3)x^2+xln3=1/2lnx

All right. Normally I'd want to place terms involving x to one side. But how do I go about doing this now when everything has x and there is that pesky x^2?
Personally I'd like to see you solve this equation if the term (ln3)x^2 was not even there.
 
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