Solving Exponential Equations with Unequal Bases question. I have it almost completely figured out but I'm stuck at the end. The question is:

You are going to purchase a new car, but being a responsible consumer means doing a little bit of research first.

First, you find the vehicle you are purchasing and its price.
Vehicle: Chevy Volt
Price: $39,145

Current interest rate: 3%

Using the function A(t)=P(1+r/n)^nt create the function that represents your new car loan that is compounded monthly.

Question

Solving Exponential Equations with Unequal Bases question. I have it almost completely figured out but I'm stuck at the end. The question is:

You are going to purchase a new car, but being a responsible consumer means doing a little bit of research first.

First, you find the vehicle you are purchasing and its price.
Vehicle: Chevy Volt
Price: $39,145

Current interest rate: 3%

Using the function A(t)=P(1+r/n)^nt create the function that represents your new car loan that is compounded monthly.

goformit100 · Answer

With due respect Welcome to Open Study ............. Sir/Ma'am @zachfluke12

anonymous · Answer

I already got that part. It is A(t)= 39,145 (1 + .03/12) ^12t.
The next part of the question is: Being a smart financial planner, you want to figure out how many months it will be until your principal is paid down to $10,000.00. Solve for t and show all of your work. Note that t will be negative because the number of months will decrease the principal.
I got this answer too. Its about -45.62≈ t.
The final part of the question is where I'm stuck though.
I'll attach it because I'm not sure how to type the equation correctly.

anonymous · Answer

Thanks @goformit100