# exponential functions

• Aug 12th 2009, 12:00 AM
Rose Wanjohi
exponential functions
solve for x where x is a real number
4+7lne(^x^2)=2e^4lnx(Cool)
• Aug 12th 2009, 02:25 AM
mr fantastic
Quote:

Originally Posted by Rose Wanjohi
solve for x where x is a real number
4+7lne(^x^2)=2e^4lnx(Cool)

The equation is not clear. Please re-post it. Ideally, learn some basic latex before re-posting: http://www.mathhelpforum.com/math-he...-tutorial.html
• Aug 12th 2009, 03:43 AM
Isomorphism
Quote:

Originally Posted by Rose Wanjohi
solve for x where x is a real number
4+7lne(^x^2)=2e^4lnx(Cool)

Guessing it is $\displaystyle 4 + 7 \ln e^{x^2} = 2e^{4\ln x}$

Use the following identities: $\displaystyle 4\ln x = \ln x^4$, $\displaystyle \ln e^{x^2} = x^2$ and $\displaystyle e^{ln x^4} = x^4$

$\displaystyle 4 + 7 \ln e^{x^2} = 2e^{4\ln x} \implies 4 + 7x^2 = 2x^4$

Now observe that $\displaystyle 4 + 7x^2 = 2x^4$ is a quadratic in $\displaystyle x^2$. Solve the equation and discard the negative root. And then the solution to the original equation is the positive square root of the root.