A rental car company charges $80 per day to rent a car and $0.10 for every mile driven. Luke wants to rent a car, knowing that: He plans to drive 500 miles. He has at most $410 to spend. Write and solve an inequality which can be used to determine d d, the number of days Luke can afford to rent while staying within his budget.

the answer to this question is in the pic

one that is bigger than 3 1/2

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: