# Solve f(x)=2 what point on graph of f g(x)=3 what point on the graph of g f(x)=g(x) do the graph of f and g intersect if so where f(x)=log 3 (x+5) and g(x)=log 3 (x-1).Please help.

beckden | Certified Educator

We are going to be using the definiton of logarithm that

`log_b(a)=c hArr b^c=a`

```f(x)=log_3(x+5)`

`f(x)=2` when

`log_3(x+5)=2`

Raising 3 to both sides gives us

`3^(log_3(x+5)=3^2`

And by the definition of logarithm

` x+5=9`

Solving for x we get

`x=4` , and we should check that answer to make sure we do not have an extraneous solution.

`f(4)=log_3(4+5)=log_3(9) = log_3(3^2)=2` so our answer checks.

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`g(x)=log_3(x-1)`

when does g(x)=3 so we have to solve

`log_3(x-1)=3`

`3^(log_3(x-1))=3^3`

`x-1=27`

So `x = 28` we should check,

`log_3(28-1)=log_3(27)=log_3(3^3)=3`

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Now we want to find when `f(x)=g(x)`

`log_3(x+5)=log_3(x-1)`

Raise 3 to both sides to get

`3^(log_3(x+5))=3^(log_3(x-1))`

`x+5 = x - 1`

Subtracting x from both sides gives us

5=-1 which is never true, so there is no place where `f(x)=g(x)` .

To recap, `f(x)=2` when `x=4, g(x)=3` when `x=28` , and there is no solution to `f(x)=g(x)`