Question

If f(x) = log(3x) and g(x) = log(x - 2), what is the value of

f(g(5))? Round to the nearest thousandth.

Answer 1

f(g(5)) = 0.156

Explanation:

We are given the following functions:

`f(x) = \log{(3x)}`

`g(x) = \log{(x-2)}`

f(g(5))?

First we find g(5), and then, we find f when
`x = g(5)`. So

`g(5) = \log{(5-2)} = \log{3} = 0.477`

`f(g(5)) = f(0.477) = \log{3*0.477} = 0.156`

So

f(g(5)) = 0.156