Question

For what values of b will f(x) = logb x be a decreasing function?

Answer 1

the answer to this is 0<b<1

Answer 2

You are given the logarithmic function $f(x)=\log_bx.$ Note that this function is defined when:

1. $b>0,\ b\neq 1;$
2. $x>0.$

This function is increasing, when $b>1$ and decreasing when $0<b<1$ (see attached graphs for details).

Answer: $0<b<1.$