Dave must buy a practical and reliable family vehicle. He decides to purchase a

Question

Dave must buy a practical and reliable family vehicle. He decides to purchase a small family sedan for $20000 (after taxes), knowing that it will depreciate 18% each year. Mark, one of dave's coworkers decides to purchase a classic muscle car for $13000 (after taxes)/ he knows that it will appreciate 6% each year. If dave buys his car 5 days later, when will the cars be worth the same amount of money.
B) repeat 'A' but if mark buys his car 2 days before dave does.

I know how to do logs and how to solve, i just need the setup. So thats all i want and explain why it would be so and so to the power of x+2 or x-2, etc.
Ex) I know it 20000(0.82)^x=13000(1.06)^x but i dont know which one you add 5 to or subtract 5 to (for the x value)

Explanation / Answer

20000(1-0.18)^((x+5)/365) = 13000(1+0.06)^(x/365) 20/13 (1-0.18)^((x+5)/365) = (1+0.06)^(x/365) applying log on both sides and solving log (20/13) + ((x+5)/365) log(0.82) = (x/365) log(1.06) x =606.9 days = 607 days 20000(1-0.18)^((x+2)/365) = 13000(1+0.06)^(x/365) 20/13 (1-0.18)^((x+2)/365) = (1+0.06)^(x/365) applying log on both sides and solving log (20/13) + ((x+2)/365) log(0.82) = (x/365) log(1.06) x =610.934 days = 611 days

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