1. ## Evaluating logs

Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

2. Originally Posted by math619
Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

a) Which is it? 3200 or 320000? I get 5 for the first and 11.6439 for the second.

b) $log_55 = 1$ so $log_2 2^{log_55} = log_2 2 = 1$

-Dan

3. Originally Posted by math619
Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

I have no time to explain long, but here is quick one way of doing your problems here.

a) Log(to the base 2)[3200] -2Log(to the base 2)[10]
= Log(base 2)[3200 / (10^2)]
= Log(base 2)[32]

b) Log(base 2)[2 raised to Log(base 5)[5]]
= Log(base 2)[2 raised to 1]
= Log(base 2)[2]

In about 12 to 14 hours from now I can explain any other way, including your changing into base 10 first---if you like.

4. Here's the method for a):

$log_2(3200) - 2 log_2(10)$

$= log_2(3200) - log_2(10^2)$

$= log_2(3200) - log_2(100)$

$= log_2 \left ( \frac{3200}{100} \right )$

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

-Dan