Question

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

Answer 1

f(x)=12^x , just took the test

Explanation:

Answer 2

Denise creates the exponential function
`g(x)=12 ^(x)`

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
`12 ^(x)=a` ("for what value of x, is 12 to the power of x equal to a?")

this expression is equivalent to
`x=log_1_2(a)`,

(so 12 to the power of x is a, for x=
`log_1_2_(a)`)

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:


`f(x)=log_1_2(x)`

(example: we want to calculate at which value is
`12^(x)` equal to 5?
answer: f(x)=
`log_1_2(5)`,

check:
`12^(log_1_2(5)) =5`, which is true, by properties of logarithms)


Answer: log_1_2(x) (B)