Step-by-step explanation
We are told that each year the value of the laptop is 75% of the value of the value of the previous year. This means that every year the current value of the laptop is multiplied by 0.75. Then if v is the original value of the laptop its value after t years is given by:

We need to find after which year V(t) is equal to 500 or less then we have V(t)≤500 and since the original value of the laptop was 4200 we have v=4200:

We divide both sides by 4200:

Then we apply the logarithm to both sides:

Then we use the property of logarithm regarding exponents:
![\begin{gathered} \operatorname{\log}_(10)(0.75^(t))\leqslant\operatorname{\log}_(10)((5)/(42)) \\ t\log_(10)(0.75)\leq\operatorname{\log}_(10)((5)/(42)) \end{gathered}]()
And we divide both sides by the logarithm of 0.75 (we change the inequality symbol because log(0.75) is negative):
![\begin{gathered} \frac{t\operatorname{\log}_(10)(0.75)}{\operatorname{\log}_(10)(0.75)}\ge\frac{\log_(10)((5)/(42))}{\operatorname{\log}_(10)(0.75)} \\ t\ge\frac{\log_(10)((5)/(42))}{\operatorname{\log}_(10)(0.75)} \end{gathered}]()
Then we get:

So the laptop's value is less than $500 after 7.398 years.
Answer
Since we are requested to write a whole number as the answer and the smallest whole number that is bigger than 7.398 is 8 we have that the answer is 8 years.