Yes, the logarithm of any positive number less than 1 is negative.

Example on your TI-84,

log(.9) = -.0457574906

However, logarithms can only be taken of positive numbers in the
course you are taking.

[If you study higher mathematics, you will learn that logarithms of negative
numbers are imaginary numbers.  That's why if you put your TI-84 in a+bi
mode, that log(-2) = .3010299957+1.36437654i, but you will never run into that
in the course you are now taking.  So as far as you are concerned now,
logarithms can only be taken of positive numbers.  However the logarithms
themselves can indeed be negative.)

Edwin