The logarithmic function f(x) = ln x is transformed to g(x) = In(x − 2) + 5. Which of the following is true? A. f(x) is translated up 5 units.
B. f(x) is translated down 2 units.
C. f(x) is translated left 2 units.
D. f(x) is translated right 5 units.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: