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# (x-1)^log(x-1)=100(x-1) How do you solve this?

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- ¿ /\/ 馬 ?Lv 71 decade agoBest Answer
(x-1)^log(x-1)=100(x-1)

Log both sides

log(x-1)*log(x-1) = log(100(x-1))

log(x-1)*log(x-1) = log100 + log(x-1)

2log(x-1) = 2 + log(x-1)

2log(x-1) - log(x-1) = 2

log(x-1) = 2

log(x-1) = 2, which can be written as

10^2 = x-1

100 = x-1

x= 101

Notes: log(xy) = logx + logy

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