If denise wanted to create a function that modeled an exponential function with base of 12 and what exponents were needed to reach specific values, how would she set up her function?
f(x) = x12
f(x) = log12x
f(x) = 12x
f(x) = logx12

Denise creates the exponential function 

assume she want to find for what value of x, her function reaches the value, 3, or 8.2, or any value a (larger than 0)

so she shants to solve    ("for what value of x, is 12 to the power of x equal to a?")

this expression is equivalent to , 

(so 12 to the power of x is a, for x=)

we can generalize this result by creating a function f.

In this function we enter x, the specific value we want to reach. f will calculate the exponent needed, in the following way:

 

(example: we want to calculate at which value is equal to 5?
f(x)= ,

check:, which is true, by properties of logarithms)

log_1_2(x)       (B)