Question

Which of the following is the inverse of y = 2^3x + 1

Answer 1

The choices are missing, but we can find the right answer by using the given function

The inverse of  $y=2^{3x}+1$  is  $y=\frac{1}{3}[\frac{log(x-1)}{log(2)}]$

Step-by-step explanation:

Let us revise the steps of finding the inverse of a function

1. Write the function in the form of y = f(x)
2. Switch x and y
3. Solve to find the new y

∵ $y=2^{3x}+ 1$

- Switch x and y

∴ $x=2^{3y}+1$

- Subtract 1 fro both sides

∴ $x-1=2^{3y}$

- Insert ㏒ in both sides

∴ $log(x-1)=log(2^{3y})$

- Remember $log(a^{n})=n.log(a)$

∵ $log(2^{3y})=(3y).log(2)$

∴ $log(x-1)=(3y).log(2)$

- Divide both sides by ㏒(2)

∴ $\frac{log(x-1)}{log(2)}=3y$

- Divide both sides by 3

∴ $\frac{1}{3}[\frac{log(x-1)}{log(2)}]=y$

- Switch the two sides

∴ $y=\frac{1}{3}[\frac{log(x-1)}{log(2)}]$

The inverse of  $y=2^{3x}+1$  is  $y=\frac{1}{3}[\frac{log(x-1)}{log(2)}]$

Learn more:

You can learn more about the logarithmic function in brainly.com/question/11921476

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