Help with Logs

[Krahe]

I'm taking Cal III, and it has been 3 years since I have taken the previous course so my skills are a little rusty. The equation is,

r(t)= (e^t) i +(2/9) e^(2t) j at t=ln3

The question wants this equation in terms of x and y and then evaluate the velocity and acceleration vectors and the given value of t. Finding v(t) and a(t) is easy, but I'm having trouble working with logs.

This is my thought process for tackling the problem;
The question wants this equation in terms of x and y. Since i is x and j is y; I would set x= e^t and y= (2/9) e^(2t).

[FONT=Roboto, arial, sans-serif]Solving for t from the x equation; Take the natural log of both sides. therefore t=ln(x)
[/FONT]plugging that into y

y= (2/9) e^(2(ln(x))).

I checked the solution Manual and the answer provided was that y= (2/9) x^2.

Where did I mess up? Any Help would be greatly appreciated.

 

[Krahe]

Homework help

It's been 3 years since I've taken my last math course, and I'm struggling with this problem

Any help would be appreciated!

 

[Deleted member 4993]

I'm taking Cal III, and it has been 3 years since I have taken the previous course so my skills are a little rusty. The equation is,

r(t)= (e^t) i +(2/9) e^(2t) j at t=ln3

The question wants this equation in terms of x and y and then evaluate the velocity and acceleration vectors and the given value of t. Finding v(t) and a(t) is easy, but I'm having trouble working with logs.

This is my thought process for tackling the problem;
The question wants this equation in terms of x and y. Since i is x and j is y; I would set x= e^t and y= (2/9) e^(2t).

Solving for t from the x equation; Take the natural log of both sides. therefore t=ln(x)
plugging that into y

y= (2/9) e^(2(ln(x))) → = (2/9) e^(ln(x^2) = 2/9 * x^2

I checked the solution Manual and the answer provided was that y= (2/9) x^2.

Where did I mess up? Any Help would be greatly appreciated.

You did not mess up anywhere - just did not carry through to "required" display!!

 

[stapel]

r(t)= (e^t) i +(2/9) e^(2t) j at t = ln3

...The question wants this equation in terms of x and y. Since i is x and j is y; I would set x= e^t and y= (2/9) e^(2t).

Solving for t from the x equation; Take the natural log of both sides. therefore t = ln(x), plugging that into y

y= (2/9) e^(2(ln(x))).

I checked the solution Manual and the answer provided was that y= (2/9) x^2.

What are the rules for log expressions? (here) Use the appropriate rule to move the "2" inside the log.

What is the definition of "logarithm"? Read this page (down to the bottom!) to figure out the fiddly bit that you've forgotten.

 

[Krahe]

What are the rules for log expressions? (here) Use the appropriate rule to move the "2" inside the log.

What is the definition of "logarithm"? Read this page (down to the bottom!) to figure out the fiddly bit that you've forgotten.

Thanks!

 

[Krahe]

You did not mess up anywhere - just did not carry through to "required" display!!

Thanks!