Question

For what values of b will f(x)= log b^x be an increasing function?

Answer 1

$log(b^x) = xlog(b)$

This is basically a line with slope $log(b)$

For this to be an increasing function, the slope has to be greater than 0.

$log(b) \ \textgreater \ 0\\ b \ \textgreater \ 10^0\\ b \ \textgreater \ 1$

So f(x) will be an increasing function for all b > 1

Answer 2

Using logarithmic function concepts, it is found that for values of b > 1, $f(x) = \log_b{x}$ will be an increasing function.

What is an logarithmic function?

A logarithmic function is modeled by:

$f(x) = \log_b{x}$

The coefficient b determines the behavior of the function, as follows:

• b > 1: The function is increasing.

• b < 1: The function is decreasing.

Hence, for values of b > 1, $f(x) = \log_b{x}$ will be an increasing function.

More can be learned about logarithmic function concepts at https://brainly.com/question/25537936