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

Answer 1

(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