Hello I am new and I need help with my homework as soon as possible please thank you

Question

1.) Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 2, reflected across the x-axis, and shifted by 4 units right.

A.) g(x) = −2ln (x − 4)

B.) g(x) = 2ln (x − 4)

C.) g(x) = −2ln (x + 4)

D.) g(x) = 2ln (x + 4)

2.) Simplify ln e −12t .

A.) −12

B.) 12t

C.) −12t

D.) 12

hi please help and explain/solve thanks

Answer 1

1. A

-2 reflects across the x-axis and stretches vertically by 2.

- 4 shifts 4 units right, opposite the sign

2. C

This one is a little more vague. the natural log of e is 1, and 1 to any power is just 1, buuuuut you use this to solve for t in an equation, like...

e^-12t = 3

ln(e^-12t) = ln(3)

-12t = ln(3)

etc...