# Math Help - exponential functions

1. ## exponential functions

solve for x where x is a real number
4+7lne(^x^2)=2e^4lnx

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

3. Originally Posted by Rose Wanjohi
solve for x where x is a real number
4+7lne(^x^2)=2e^4lnx
Guessing it is $4 + 7 \ln e^{x^2} = 2e^{4\ln x}$

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

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

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