Question

What is the logarithmic function modeled by the following table?

x f(x)
8 3
16 4
32 5

Answer 1

`f(x) = log_2(x)`

Explanation:

We can see that x values are 2 raised to the power f(x)

For example, for f(x) = 3, x = 2^3 = 8

f(x) = 4, x = 2^4 = 16

Let's substitute f(x) with y to make it easier to comprehend

We then get

`x = 2^y\\`

Take log₂ on both sides

`\log_(2)x = \log_2{(2^y)}\\\\\log_2(2^y) = y\\`

So we get

`\log_2(x) = y\\\\y = \log_2(x)\\\\f(x) = \log_2(x)`