solve: 6^n+1 >= 10 round to four decimal places?

Question

a. n>= 0.2851
b. n>= 0.6667
c. n>= 1.2851
d. n>= -0.7782

Answer 1

6^n + 1 >= 10
6^n >= 9 (subtract 1 from each side)
n log 6 >= log 9 (take logarithm of each side)
n >= log 9 / log 6 (divide by log 6)
n >= 1.2263

That doesn't seem to match any of your answers, but (c) is the closest.

The answer is clearly just barely over 1 (because 6^1+1 = 7, which is slightly under ten, while 6^2+1 = 37, which is well over ten). (c) is also the only answer on your list greater than one.