Which of the following options is an equivalent function to f(x) = 3(2)3x?
A.f(x)= 3(8)x
B.f(x)= 24x
C.f(x)= 27(8)x
D.f(x)= 3(8x)
To find an equivalent function to f(x) = 3(2)3x, we need to simplify the expression. The expression 3(2)3x means multiplying three terms: 3, 2, and 3x.
First, let's simplify 3(2) to get the base value:
3(2) = 6
Now, let's rewrite the expression using the simplified base value:
f(x) = 6 * 3x
Since the base value is 6, the equivalent function should have 6 in it. Looking at the provided options, the only option that contains 6 is option B: f(x) = 24x.
So, the correct answer is B. f(x) = 24x.
To determine which of the given options is an equivalent function to f(x) = 3(2)3x, we need to simplify the expression.
The given function can be written as f(x) = 3 * 2^3 * x. This is because raising the base 2 to the power of 3 gives 2^3 = 8.
Now, let's compare the options:
A. f(x) = 3(8)x = 24x
In this option, we have 3 multiplied by 8, which is 24. This is the same as 3 * 2^3. The answer is 24x.
B. f(x) = 24x
This option is already simplified and matches the answer from option A.
C. f(x) = 27(8)x
In this option, we have a different base of 27 instead of 2. Therefore, it is not equivalent to the given function.
D. f(x) = 3(8x)
In this option, we have 8 multiplied by x inside the parentheses, which is not the same as 2^3 multiplied by x. Therefore, this is not equivalent to the given function.
Based on the analysis above, the correct option is B. f(x) = 24x, which is equivalent to f(x) = 3(2)3x.
You have weird notation. Using ^ for exponents,
3^2^3 = 3^8
so I guess (A)