1. ## 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!

2. 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.

3. Hi thanks for the reply

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?

4. Ok, I got it on the first one.

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

$\displaystyle logx/loga$

5. 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.

6. 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

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

Hence,

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

Question 2

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

Hence,

$\displaystyle 2^x = 3$

$\displaystyle \Leftrightarrow x = \log_2 3$

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

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

7. Originally Posted by DivideBy0
Hi nugiboy!

Question 1

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

Hence,

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

Question 2

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

Hence,

$\displaystyle 2^x = 3$

$\displaystyle \Leftrightarrow x = \log_2 3$

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

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

8. Here are the ones that I use:

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

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

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

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

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

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

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

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

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

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

9. 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.

10. 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. $\displaystyle \log_a b^n = n\log_a b$

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

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

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

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

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

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

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

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.