lim as x->1 from the negative side means that x is a little less than 1.

(x-1) is a very small negative number.

1/(x-1) is 1/(a very small negative number), which is a very big negative number

2^(1/(x-1)) is 2^(a big negative number), which is a small positive number (exponential graph 2^x has horizontal asymptote of 0).

1-2^(1/(x-1)) is just 1-a small positive number, or a number just less than 1.

log[base 3](1-2^(1/(x-1))) is just log[base 3](a number just less than 1), which is a very small negative number (log(something < 1) is negative).

1/log[base 3](1-2^(1/(x-1))) is just 1/a very small negative number, which is a large negative number.

if x->1 and gets infinitely close to 1 from the left, then 1/log[base 3](1-2^(1/(x-1))) approaches negative infinity.