Answer: x = (log(y) /(400 log1.0065) or x = log(initial cost)/1.126
Step-by-step explanation: Take the log of both sides of your equation:
log(y) = log(400)(1.0065)^x
log (y) = log 400 + log(1.0065)^x
Subtract log(400) from both sides:
log(y) - log 400 = xlog(1.0065)
Divide both sides by log(1.0065)
[log(y) - log(400)]/log(1.0065) = x
Now, if you want to know how many years it will take for the guitar to be worth $200, replace y with 200 and solve.