Question

Compare the graphs of the logarithmic functions
`f(x)=log_7(x)` and
`g(x)=log_4(x)`. For what values of
`x` is
`f=g`,
`f\ \textgreater \ g`, and
`f\ \textless \ g`? Explain how you know.

Answer 1

check the picture below.

keeping in mind that, log(x) has a domain of x > 0, namely, it will never spit out a number that's 0 or negative, therefore, both graphs go down down and down ever closer and closer to x = 0, but never getting there, and while racing down, f(x) is above g(x), thus is higher.