Which of the following uses the properties of logarithms to correctly rewrite f(x) = log, 16x3? (1 po
• f(x) = 310g2 x + 4
f(x) = 10g2 3x + 4
• f(x) = 16 10g2 23
• f(x) = 310g2 x + 12
The correct answer is f(x) = 3 log2 (16x).
To simplify the given expression f(x) = log(16x^3), we can apply the following properties of logarithms:
1. log(a*b) = log(a) + log(b)
2. log(a^n) = n*log(a)
3. log(1) = 0
Using these properties, we can rewrite f(x) as follows:
f(x) = log(16x^3)
= log(2^4 * x^3) (16 can be written as 2^4)
= log(2^4) + log(x^3) (using property 1)
= 4*log(2) + 3*log(x) (using property 2)
= 3*log(x) + 4*log(2)
Therefore, the correct answer is f(x) = 3 log2 (16x).