Here we want to find similarities between the graphs of f(x) and g(x). We will see that both graphs have the same behavior and f(x) is just a vertical dilation of g(x).
First, we know that:
[tex]f(x) = log_2(x)\\\\g(x) = log_{10}(x)[/tex]
Remember the general rule:
[tex]log_a(x) = \frac{ln(x)}{ln(a)}[/tex]
Then we can rewrite:
[tex]f(x) = \frac{ln(x)}{ln(2)} \\\\g(x) = \frac{ln(x)}{ln(10)}[/tex]
So we can see that both functions depend linearly on ln(x), so we have already one similarity between these two functions.
The only difference comes from a multiplicative constant, such that we can write:
[tex]f(x) = \frac{ln(10)}{ln(2)}*g(x)[/tex]
So f(x) is a vertical dilation of g(x), but the general shape of both graphs is exactly the same, as you can see in the image below, where the blue graph is the one of f(x).
If you want to learn more about logarithmic functions, you can read:
https://brainly.com/question/13473114
