# Thread: [SOLVED] Find equation of y in terms of x?

1. ## [SOLVED] Find equation of y in terms of x?

If x = e^3t & y = e^t, where e is exponential number

Find equation of y in terms of x?
Ans: y^3 = 3x

These are my steps:
x = e^3t
(or) e^(ln x) = e^3t
(or) ln x = 3t
(or) t = (ln x)/3 ------(i)

y = e^t
(or) e^(ln y) = e^t
(or) ln y = t
(or) ln y = (ln x)/3 ------Using (i)

What to do after this???

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EDIT: Question NULL & VOID

2. Hello,

That's pretty weird... Is it $\displaystyle x=e^{3t}$ and $\displaystyle y=e^t$ ?

If so, then remember this property : $\displaystyle a^{bc}=(a^b)^c=(a^c)^b$

Therefore $\displaystyle x=e^{3t}=(e^t)^3=y^3$

3. Hello Moo.
The original question was a mechanics question. It stated:
A body starts from origin with velocity V = (e^3t)i + (e^t)j. Then find the equation of trajectory of the body?

Ans: y^3 = 3x
i - unit vector along x-axis
j - unit vector along y-axis
Was my interpretation of the question wrong?

EDIT: I messed up. dx/dt = e^3t and dy/dt = e^t.
Which gives x = e^(3t)/3 and y = e^t
And using the obvious property which Moo stated(instead of doing the rubbish I did by taking natural log), x = (y^3)/3