Question

Compare the graphs of the logarithmic functions e="f(x)=log_7(x)" alt="f(x)=log_7(x)" align="absmiddle" class="latex-formula"> 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.