Question

due friday by 11:59pm points 100 submitting an external tool exam 3 100 points possible answered: 3/14 question 4 evaluate the following expressions. (a) \\(\log_{2} 2^{11} = \\) (b) \\(\log_{2} 16 = \\) (c) \\(\log_{5} 125 = \\) (d) \\(\log_{6} 6^{9} = \\) question help: message instructor next question

Explanation:

Part (a)

Step1: Recall log property

Use the property $\log_a a^x = x$.

Step2: Apply to expression

For $\log_2 2^{11}$, $a = 2$, $x = 11$, so result is 11.

Part (b)

Step1: Rewrite 16 as power of 2

$16 = 2^4$.

Step2: Apply log property

$\log_2 2^4 = 4$ (using $\log_a a^x = x$).

Part (c)

Step1: Rewrite 125 as power of 5

$125 = 5^3$.

Step2: Apply log property

$\log_5 5^3 = 3$ (using $\log_a a^x = x$).

Part (d)

Answer:

11