Tony buys a car for £ 10100. Its value decreases by 42 per cent each year. How long will it take
for the value to drop to £ 9750? Give your answer in years to 2 decimal places and show your working.
Value after $x$ years = $$10100 \times (0.58)^x = 9750$$
$$\Rightarrow x=\log_{0.58}(0.9653)$$
$$\Rightarrow x=0.06.$$