converting parametric equasions to cartesian, slightly confused

I've missed a few days of class due to illness and have fallen behind a bit. There is homework due and I have figured everything out but this.

x(t)=e^7t

y(t)=e^4t

I have completely forgotten how to get a variable out of the exponent... >_<

Re: converting parametric equasions to cartesian, slightly confused

Quote:

Originally Posted by

**Kisolv** I've missed a few days of class due to illness and have fallen behind a bit. There is homework due and I have figured everything out but this.

x(t)=e^7t

y(t)=e^4t

I have completely forgotten how to get a variable out of the exponent... >_<

$\displaystyle \begin{cases}y(t)=e^{4t} \\x(t)=e^{7t}\end{cases}$

hence :

$\displaystyle y=(e^t)^4=(e^{7t})^{\frac{4}{7}}=x^{\frac{4}{7}}$

Re: converting parametric equasions to cartesian, slightly confused

Another way:

$\displaystyle \ln x = \ln {e^{7t}}=7t \Leftrightarrow t = \frac{\ln{x}}{7}$

$\displaystyle y = e^{4t} = e^{\frac{4}{7}\ln{x}}=e^{\ln{x}^{4/7}}=x^{4/7}$