Beth and darcy are each driving a car. they start at the same location and will be driving the same route. beth's car has a gas tank that can hold 15 gallons of gas. her car uses 1 30 of a gallon of gas per mile driven. darcy's car has a gas tank that can hold 16 gallons of gas. his car uses 1 25 of a gallon of gas per mile driven. both cars start with full tanks of gas. after how many miles will both cars have the same number of gallons of gas remaining in their gas tanks?

think about it deeply and passionately about this property

i am sorry

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places