Question

Can some please explain why this is wrong, and what is the correct answer

Answer 1

Explanation:

Firstly let's just simplify the expression to:
`log_5(x^3)=1`

From here the domain needs to be positive and not zero, since the cubic is only positive for positive values. So your domain is correct

Now for the solution part, we can rewrite the log into exponential form as such:
`5^1=x^3`

and from here we can take the cube root to get:
`x=\sqrt[3]{5}`

so both of your answers look correct, and I would recommend asking your teacher about this as it may be a mistake.