Question

Graph y=log8x and its inverse.

Answer 1

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!

Answer 2

Answer:

The answers are:

Graph: in the attached image

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

Step-by-step 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 $a^c=b$

$y=log(8x)\\10^y=8x\\x=\frac{10^y}{8} \\x=(5*2)^y*2^-^3\\x=5^y*2^y*2^-^3\\x=5^y*2^y^-^3$

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:$f^-^1(x)=5^x*2^x^-^3$