# Thread: inequality symbol reverse with logs question

1. ## inequality symbol reverse with logs question

Hello

I have an inequality where I have this equation:

0.79^n < 0.1

I assumed that if I take logs of both sides the result would be:

n log 0.79 < log 0.1

n < log 0.1 / log 0.79

n < 9.768

But actually result should be n > 9.768

Why is the inequality symbol reversed in this situation?

Angus

2. As $\log(0.79) < 0$ you have to reverse the direction of the inequality when dividing by negative numbers