William the Spirit buys a laptop for € 1,300 . Every year he write off 10% of the purchase price. After how many years the laptop still € 52

We have this....10% off of something is just 90% of its valued = .90 .....thus.....

520 =  1300(.90)ⁿ   where n is the number of years

Divide both sides by 1300

520/1300  = (.90)ⁿ       take the log of both sides

log(520 / 1300) = log(.90)ⁿ     and by a log property, we can write

log(520 / 1300) = n log (.90)       divide both sides by log(.90)

log(520 / 1300) / log(.90)  = n = about 8.7 years