# Log help needed!

• January 4th 2008, 06:29 AM
nugiboy
Log help needed!
Hi there!

Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

1. Write Log25 + Log21.6 as an integer.

2. Solve the equation 2^x = 3

And if you could sort of summarise or give a link with an explanation of logs it would be great.
Thanks!
• January 4th 2008, 06:38 AM
mathgeek777
Quote:

Originally Posted by nugiboy
Hi there!

Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

1. Write Log25 + Log21.6 as an integer.

2. Solve the equation 2^x = 3

And if you could sort of summarise or give a link with an explanation of logs it would be great.
Thanks!

Someone correct me if I'm wrong, but for one, I believe, since they're both taking the log of 2, that you can simply add the two together, giving you the log 2 of 3.6.

For two, take the log of 2 of both sides. It'll isolate x, and you should be able to solve it on a calculator.
• January 4th 2008, 06:43 AM
nugiboy

I checked in the answer, and its 3, which your method doesn't work out to be. Thanks for trying though. Your second answer worked.

Can anyone else just verify?
• January 4th 2008, 06:52 AM
mathgeek777
Ok, I got it on the first one.

Use the change of base formula on both equations, and add them together.

$logx/loga$
• January 4th 2008, 07:01 AM
nugiboy
Not quite sure about the change of base equation. Could someone explain to me in a bit more detail why and how it works etc. Sorry for being picky. Thanks though.
• January 4th 2008, 07:02 AM
DivideBy0
Quote:

Originally Posted by nugiboy
Hi there!

Im a bit confused on the rules of logs, and im a bit stuck on this 2 part question.

1. Write Log25 + Log21.6 as an integer.

2. Solve the equation 2^x = 3

And if you could sort of summarise or give a link with an explanation of logs it would be great.
Thanks!

Hi nugiboy!

Question 1

$\log_a x + \log_a y = \log_a {xy}$

Hence,

$log_2 5+\log_2 1.6 = \log_2 8 = 3$

Question 2

If $a^x = b$, then $\log_a b = x$

Hence,

$2^x = 3$

$\Leftrightarrow x = \log_2 3$

If you want to evaluate on a calculator, use $\frac{\log_a b}{\log_a c}=\log_c b$

$\Rightarrow \log_2 3 = \frac{\log_{10} 3}{\log_{10} 2}\approx 1.58$
• January 4th 2008, 07:10 AM
nugiboy
Quote:

Originally Posted by DivideBy0
Hi nugiboy!

Question 1

$\log_a x + \log_a y = \log_a {xy}$

Hence,

$log_2 5+\log_2 1.6 = \log_2 8 = 3$

Question 2

If $a^x = b$, then $\log_a b = x$

Hence,

$2^x = 3$

$\Leftrightarrow x = \log_2 3$

If you want to evaluate on a calculator, use $\frac{\log_a b}{\log_a c}=\log_c b$

$\Rightarrow \log_2 3 = \frac{\log_{10} 3}{\log_{10} 2}\approx 1.58$

Hey thanks for that. I think i understand a bit better now. Do you know if there are any other necessary rules i should know about logs as im doing an As level math paper in a couple of weeks. What about dividing, taking away, and other equations?
• January 4th 2008, 07:38 AM
DivideBy0
Here are the ones that I use:

Note that we normally assume that a, b, c, and d are positive.

1. $\log_a b^n = n\log_a b$

2. $\log_ab+\log_ac=\log_a{bc}$

3. $\log_a b - \log_a c=\log_a{\left( \frac{b}{c}\right)}$

4. $-\log_ab=\log_a{\left(\frac{1}{b}\right)}$ (derived from 3)

5. $(\log_ab)(\log_cd)=(\log_ad)(\log_cb)$

6. $\frac{\log_ab}{\log_ac}=\log_cb$

7. $\log_ab=\frac{1}{\log_ba}$

8. $\log_{a^n} b^n=\log_a b$

You may only need the first four if you're studying basic logarithms, but the others are also incredibly useful.
• January 4th 2008, 07:51 AM
Krizalid
Quote:

Originally Posted by DivideBy0
Note that we normally assume that a, b, c, and d are positive.

Of course we require that logarithm base must be greater or equal than 2.

:D
• January 4th 2008, 08:41 AM
nugiboy
Quote:

Originally Posted by DivideBy0
Here are the ones that I use:

Note that we normally assume that a, b, c, and d are positive.

1. $\log_a b^n = n\log_a b$

2. $\log_ab+\log_ac=\log_a{bc}$

3. $\log_a b - \log_a c=\log_a{\left( \frac{b}{c}\right)}$

4. $-\log_ab=\log_a{\left(\frac{1}{b}\right)}$ (derived from 3)

5. $(\log_ab)(\log_cd)=(\log_ad)(\log_cb)$

6. $\frac{\log_ab}{\log_ac}=\log_cb$

7. $\log_ab=\frac{1}{\log_ba}$

8. $\log_{a^n} b^n=\log_a b$

You may only need the first four if you're studying basic logarithms, but the others are also incredibly useful.

Thanks very much. I think ive got everything i need there. I still need to work through them to make sure i understand them. Just wondering if any of the formulas you gave allow you to work with logs which don't have the same base.