Question

Graph y=log8x and its inverse.

Answer 1

The answers are:

Graph: in the attached image

Inverse function:
`f^-^1(x)=5^x*2^x^-^3`

Explanation:

In order to get the graph with both functions, we have to determine the inverse function of
`y=log(8x)`

The steps are:

1. we have to free the "x" variable.
2. Then we have to invert the "y" and "x" variables.
3. Finally, the "y" variable is called
   `f^-^1(x)`

So, first, we applicate the next property:

If
`log_a(b)=c`, so
`a^c=b`

`y=log(8x)\\10^y=8x\\x=(10^y)/(8) \\x=(5*2)^y*2^-^3\\x=5^y*2^y*2^-^3\\x=5^y*2^y^-^3`

Then, we invert the variables:

`y=5^x*2^x^-^3\\f^-^1(x)=5^x*2^x^-^3`

I have attached an image that shows the graph of both functions.

In red:
`y=log(8x)`

In blue:
`f^-^1(x)=5^x*2^x^-^3`

Answer 2

The inverse of y = log (8x) would be:

y=Log8^x=xlog8=xlog2^3=3xlog2

y=3log2 * x

the inverse function is

x=3log2*y

y=x/3log2

I hope my answer has come to your help. God bless and have a nice day ahead!