The efficiency e of a gasoline engine as a function of its compression ratio r is given by e =1− r^(1−γ) , where γ is a constant.

Find γ for e = 0.55 and r = 7.5

so you are solving,

.55 = 1 - (7.5)^(1-y)
7.5^(1-y) = .45
take log of both sides, and use rules of logs
(1-y)log 7.5 = log .45
1-y = log .45/log7.5

y = 1 - (log.45/log7.5)

I got appr 1.3963