Equating equations with a common variable exponent in each

1.06^x=3.4(1.02)^x    divide both sides by (1.02)^x

[ 1.06 ] ^x  / [ 1.02]^x    = 3.4      and we can write this as

[ 1.06 / 1.04 ] ^x   =  3.4           simplify

[ 53 / 51 ] ^x   = 3.4      take the log of both sides

log [ 53/51 ]^x  = log  [ 3.4]      divide both sides by log [53/51]

x =  log [ 3.4] / log [ 53 / 51]  ≈  31.814