p=1-r^1-y where y is a constant, find y for p=0.55 and r=7.5

p=1-r^1-y where y is a constant, find y for p=0.55 and r=7.5

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OK...so I assume we have

.55 =1 -7.5^(1-y)                 subtract 1 from both sides

-.45 =- 7.5^(1-y)                 multiply both sides by  -1

.45 = 7.5^(1-y)                    take the log of both sides

log .45 =log 7.5^(1-y)          and by a log property we can bring the (1-y) "out front" on the right

log .45 = (1-y)log 7.5            divide both sides by log 7.5

(log .45 / log 7.5) = 1 - y      add y to both sides and subtract (log .45 / log 7.5) from both sides

y = 1 - (log .45 / log 7.5)

y ≈ -1.3963

Check this for yourself to see that it "works" !! ........

r^1 is just r

so

p=1-r-y

0.55=1-7.5-y

0.55=-6.5-y

y=-6.5-5.5 = -12