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### Using a Rule of Logarithms

```
Date: 9/13/95 at 22:12:37
From: Anonymous
Subject: Math problem--I need help

I am a 9th grader and taking Algebra II.  I can't figure out this problem.
Can you help?

log(sub)2 3k+log(sub)2 5=log(sub)2 45.  Thanks, doc.

Joey Jackson
```

```
Date: 9/14/95 at 9:34:9
From: Doctor Ethan
Subject: Re: Math problem--I need help

Well, here is what you do.

First you need to realize a rule about logs. Assuming they have the same base,
this is always true.

Log a + Log b = Log a * b

So we can take your problem (I am going to leave off the base two stuff)

and we have

Log 3k + log 5 = log 45

but by our formula we have log (3k) (5)  = log 45

This is  Log  15k = log 45

But if the log of 15k equals the log of 45 then 15k must equal 45

So we have  15k = 45

so k = 3.

Does this make sense? I hope this works for you.

- Doctor Ethan,  The Geometry Forum

```
Associated Topics:
High School Logs

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