Question

which of the following uses the properties of logarithms to correctly rewrite $f(x) = \log_{2}(32x^{6})$? (5 points)$circ$ $f(x) = 6\log_{2}x + 5LXB0circ$ $f(x) = 6\log_{2}x + 30$$circ$ $f(x) = 30\log_{2}x$

Explanation:

Step1: Split log of product

$\log_2(32x^6) = \log_2(32) + \log_2(x^6)$

Step2: Simplify $\log_2(32)$

$\log_2(32) = \log_2(2^5) = 5$

Step3: Apply power rule to $\log_2(x^6)$

$\log_2(x^6) = 6\log_2 x$

Step4: Combine the results

$f(x) = 6\log_2 x + 5$

Answer:

$f(x) = 6\log_2 x + 5$