determine the elpased time?

Question

determine the elpased time?
the half-life of sodium-24 is 14.9 hours. a hospital buys 40mg of it. how long will it take for 2.5 mg to remain

so far i got up to this point in half-life equation

2.5=40(1/2)^t/14.9 or 2.5=40(1r2)^tr14.9

Answer 1

You are right. But I want to put in a parentheses to avoid confusion: 2.5=40(1/2)^(t/14.9), or:
0.0625 = (1/2)^(t/14.9)
The rest is just math. Please take logarithm with any base (most common is with base 10):
log(0.0625) = -(t/14.9)*log(2)
Therefore: t = - 14.9*log(0.0625) /log(2) = 59.6 (hours)