Find the halflife in hours of a radioactive substance that i

Find the half-life (in hours) of a radioactive substance that is reduced by 40 percent in 45 hours.
Half life = _______(include units)

m_f = m₀ (1/2)^t/t_1/2, m_f/m₀ = 4/10, t = 45 hr

4/10 = (1/2)^(45hr)/t_1/2

log_1/2(4/10) = (45hr)/t_1/2

t_1/2 = (45hr)/(log_1/2(4/10)) = (45hr)/(ln(4/10)/ln(1/2)) = ((45hr)ln(1/2))/ln(4/10)

t_1/2 = 34.04118588147... hr 34 hr

The half-life is approximately 34 hours.