Question

1. (1/2 Points]DETAILSPREVIOUS ANSWERSOSCOLALG1 6.3.124.TUT.How is the logarithmic function f(x) = logs(x) related to the exponential function g(x) = 8*?The logarithm function is the inverse V of the exponential function.What is the result of composing these two functions and fully simplifying the result?TutorialAdditional MaterialseBookIntroduction to Logarithms

Answer 1

Answer: x

Given:

`f(x)=\log _8(x)`
`g(x)=8^x`

Let us find the composite of f(g(x))

`f(g(x))=\log _8(8^x)`

*Applying the log rule:

`\log _a(x^b)=b\log _a(x)`
`f(g(x))=x\log _8(8)`

*Applying the rule:

`\log _a(a)=1`
`f(g(x))=x(1)`
`f(g(x))=x`

The composite of f(g(x)) = x