(1.09)^n=1.9108

To find the value of an exponent, use logs.

log( 1.09ⁿ )  =  log( 1.9108 )

The exponent comes out of the log as a multiplier:

n · log( 1.09 )  =  log( 1.9108 )

Divide both sides by log (1.09 ):

n  =  log( 1.9108 ) / log( 1.09 )  =  7.51  (approximately)