# Tutor.com Exponential and Logarithmic Functions Session

##### Oct. 4, 2012

Session Transcript - Math - Algebra II, 9/28/2012 12:55PM - Tutor.comSession Date: 9/28/2012 12:55PM
Length: 31.7 minute(s)
Subject: Math - Algebra II

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Brent (Customer)
[00:00:00] simplify log2 one over two 1/2 I have read the material but I do not know how to begin to simplify this

Jinny P (Tutor)
[00:00:18] Hi. Welcome to tutor.com . My name is Jinny.

Brent (Customer)
[00:00:37] hello and aghhh

Jinny P (Tutor)
[00:00:50] It looks like we have a log base 2 problem?

Brent (Customer)
[00:01:23] yes but I don't understand what to do with the fraction

Jinny P (Tutor)
[00:01:38] Okay. Do you think you can write out the problem on the whiteboard?
[00:02:55] What were the directions to the problem? Was it just to solve it?

Brent (Customer)
[00:03:07] simplify

Jinny P (Tutor)
[00:03:21] Okay. And it wasn't equal to anything?

Brent (Customer)
[00:03:25] no

Jinny P (Tutor)
[00:03:52] Alright. So do you have an idea on how to start the problem?

Brent (Customer)
[00:05:03] I think I have to convert it to an exponential

Jinny P (Tutor)
[00:05:19] That is correct!
[00:06:01] So to make it easier to "see" we'll make your equation equal to a variable; let's say "y" and by solving for "y" we'll have the answer.

Brent (Customer)
[00:06:22] ok

Jinny P (Tutor)
[00:06:29] Can you convert the new equation into an exponential as you said?

Brent (Customer)
[00:07:46] x * log2 = 1/2

Jinny P (Tutor)
[00:08:13] Not quite...can you tell me how you got that?

Brent (Customer)
[00:08:54] the log is the exponent
[00:09:43] y = log2 1/2
[00:10:24] 2^y = 1/2

Jinny P (Tutor)
[00:10:34] Yes, that's is correct.
[00:10:40] And the next step?

Brent (Customer)
[00:12:39] isolate the variable

Jinny P (Tutor)
[00:12:50] Yup. So how would you do that?

Brent (Customer)
[00:13:37] multiply both sides by 2^y

Jinny P (Tutor)
[00:13:56] Not quite.

Brent (Customer)
[00:14:16] do we3 convert the fraction first

Jinny P (Tutor)
[00:14:21] Since we're working with logarithms, we want to utilize their properties.

Brent (Customer)
[00:14:30] ok

Jinny P (Tutor)
[00:14:43] So let's take the log of both sides of the equation.
[00:15:10] Let me put up a generic example that is similar to your problem.
[00:17:20] So both of the equations from your problem and my example are similar at the second step where I drew the arrow.

Brent (Customer)
[00:17:55] ok and the fraction

Jinny P (Tutor)
[00:18:13] The variable "x" represents the fraction.

Brent (Customer)
[00:18:41] so we substitute x for the fraction

Jinny P (Tutor)
[00:19:12] Yes, but we don't physically do it. We just take note of it.
[00:19:30] So let's continue the problem. Can you take the log of both sides and write it on the board?
[00:21:53] And the last step?
[00:23:14] Great! Now let's put 1/2 back in for "x".
[00:24:49] Awesome! Now we have to simplify this. You can simply put the value into your calculator.

Brent (Customer)
[00:25:10] what calculator

Jinny P (Tutor)
[00:25:32] Do you have a calculator you can use?

Brent (Customer)
[00:25:39] online yes

Jinny P (Tutor)
[00:26:01] Okay. So you can input log(1/2)/log(2).

Brent (Customer)
[00:26:13] I'll try

Jinny P (Tutor)
[00:26:29] Okay. Let me know what answer you get.

Brent (Customer)
[00:28:02] can I use 0.5

Jinny P (Tutor)
[00:28:07] Yup.

Brent (Customer)
[00:28:55] log 0.5 divide by log2

Jinny P (Tutor)
[00:29:02] Yes.

Brent (Customer)
[00:29:07] ok

Jinny P (Tutor)
[00:29:23] What is the final answer that you get?

Brent (Customer)
[00:29:35] -1

Jinny P (Tutor)
[00:29:44] You got it!

Brent (Customer)
[00:30:04] do we have time for one more

Jinny P (Tutor)
[00:30:36] I'm sorry but since we solved your original problem and there are other students waiting, I won't be able to do another problem with you.

Brent (Customer)
[00:31:09] ok I'll try some more and come back Thank You

Jinny P (Tutor)
[00:31:15] However, you are welcome to log back in and tell your other tutor to help you simplify a log problem with a non-10 base and they should be able to help you out.
[00:31:29] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Brent (Customer)
[00:31:31] ok