Solve the inequality 72^n^ less than = to 1/49?

Question

Thank you!

Answer 1

72^n ≤ 1/49

Pretend that there is an equal sign instead of an inequality and solve that equation first.  

You know that a^b = c is the same as log_a(c) = b so rewrite this as

log_72(1/49) = n

Since log(a/b) = log(a) - log(b) you can rewrite this as

log_72(1) - log_72(49) = n

You know that log(1) = 0 so this becomes

-log_72(49) = n

Using the change of base formula, this becomes

-ln(49)/ln(72) = n

Use a calculator to find that n = -.91 approximately.  Since the sign was originally less than or equal to, the solution is n ≤ -.91

Hope this helps you!