1-(5/6)^x>=9/10 rearrange as
1 - 9/10 ≥ (5/6)^x
1/10 ≥ (5/6)^x or
(5/6)^x ≤ 1/10 take the log of both sides
log(5/6)^x ≤ log ( 1/10) and we can write
x log(5/6) ≤ log ( 1/10) divide both sides by log(5/6).....note....since this is negative, we must reverse the inequality sign
x ≥ log (1/10) / log (5/6)
x ≥ 12.629 (approx)
1-(5/6)^x>=9/10 rearrange as
1 - 9/10 ≥ (5/6)^x
1/10 ≥ (5/6)^x or
(5/6)^x ≤ 1/10 take the log of both sides
log(5/6)^x ≤ log ( 1/10) and we can write
x log(5/6) ≤ log ( 1/10) divide both sides by log(5/6).....note....since this is negative, we must reverse the inequality sign
x ≥ log (1/10) / log (5/6)
x ≥ 12.629 (approx)