Question

Suppose the half-life of an element is 10 years. How many half-lives will it take before only about 6% of the original sample remains?

Answer 1

it will take around 40 years to get it to 6.25 precent therefore the amount of years will be between 40 and 45 years

Answer 2

the solution is to the equation (0.5)^n = 6%, where n= number of 1/2 life
after 1 half life, 0.5
after 2 ... 0.5^2 = 0.25 = 25% remaining
after 4 ... 0.5^4 = 6.25%
after 5 ... 0.5^5 = 3.125%
So answer is between 4-5 half lives.
Keep testing on your calculator till you reach about 6%.

Now using logarithms you can get a precise answer of n = ln(0.06)/ln(0.5) half lives