My course

Why wasn't x+3 used as an exponent? The answer needs to address why it was written as a factor and not as an exponent.

Hi there! I just graphed the transformed function given and I don't see anything off. Please describe the exact issue you find with the graph.

Hi there! When taking natural logarithm of (x +3)^4 we get ln (x + 3)^4 = 4 ln(x + 3).

Inverse operations: ln(e^9) = 9 and e^(ln 9) = 9 - ln and e cancel each other when we take 'ln of e' or 'e of ln'.

Inverse operations: given 4 = ln(9) we can apply e to get e^4 = 9 and back to 4 = ln(9) by applying ln. 'e' uses power form while ln uses expression format.

We can't use x + 3 as exponent because we apply 'ln'. We apply 'e' when an expression already has 'ln' that we need to get rid of.