Evaluate .1=.9^x

.1 = .9^x        take the log of both sides

log(0 1) =   log (0.9)^x        and we can write

log (0.1) = x * log (0.9)       divide both sides by log (0.9)

log (0.1)  / log (0.9)  =   x   = about  21.854

Evaluate .1=.9^x take the log of both sides,

x=log(.1) / log(.9)

x=21.85434........