Problem with Logarithms solutions

  • Thread starter Jacopo
  • Start date
  • Tags
    Logarithms
In summary, the speaker understands why they can add 2πi to logeω but is unsure why they can add 2πilogeb to logbω. Another person explains that logbω can be written as logeω over logeb and thus adding 2πi over logeb is equivalent to adding 2πi to logeω.
  • #1
Jacopo
2
0
I know why I can add [tex]2 \pi i[/tex] to [tex] log_{e} \omega [/tex]
([tex] log_{e} \omega = log_{e}z + i \theta [/tex] if [tex] \omega = z(cos \theta +i sen \theta ) [/tex]) but I can't understand why I can add [tex] \frac{2 \pi i}{log_{e}b} [/tex] to [tex] log_{b} \omega [/tex].
Does anyone have the answer for me?
Thanks!
 
Mathematics news on Phys.org
  • #2
Jacopo said:
I know why I can add [tex]2 \pi i[/tex] to [tex] log_{e} \omega [/tex]
([tex] log_{e} \omega = log_{e}z + i \theta [/tex] if [tex] \omega = z(cos \theta +i sen \theta ) [/tex]) but I can't understand why I can add [tex] \frac{2 \pi i}{log_{e}b} [/tex] to [tex] log_{b} \omega [/tex].
Does anyone have the answer for me?
Thanks!
If you know the first, the second is easy! Because
[tex]log_b(\omega)= \frac{log_e(\omega)}{log_e(b)}= \frac{log_e(\omega)+ i2\pi}{log_e(b)}= \frac{log_e(\omega)}{log_e(b)}+ \frac{2\pi i}{log_e(b)}[/tex]
 
  • #3
Oh yes :D Thanks
 

1. What are logarithms and why are they important?

Logarithms are mathematical functions that represent the relationship between a base number and its exponent. They are important because they allow for easier calculations of very large or small numbers, and are commonly used in fields such as science, engineering, and finance.

2. What is the common problem with logarithms solutions?

The most common problem with logarithms solutions is when the base of the logarithm is not specified or is not clear. This can lead to confusion and incorrect calculations.

3. How do you solve problems with logarithms?

To solve problems with logarithms, you must first identify the base of the logarithm and then use the appropriate logarithm rules to simplify the expression. This may involve converting between exponential and logarithmic form, using the product or quotient rule, or applying the power rule.

4. What are some common mistakes when working with logarithms?

Some common mistakes when working with logarithms include forgetting to apply the logarithm rules, using the wrong base for a logarithm, and incorrectly converting between exponential and logarithmic form. It is important to carefully check your work and be familiar with the rules before attempting to solve logarithm problems.

5. Are there any real-life applications of logarithms?

Yes, logarithms have many real-life applications. They are commonly used in finance to calculate compound interest, in science to measure the intensity of earthquakes and sound, and in engineering to express signal strength and decibel levels. They are also used in computer science for data compression and in biology to measure pH levels.

Similar threads

MHB Logarithmic Equation solve log_(3x)3+log_(x/3)3=5/12
    • General Math
Replies
1
Views
924
B Characteristics of the parent logarithmic function
    • General Math
Replies
4
Views
2K
MHB How Do I Solve a Logarithmic Equation with Different Bases and Variables?
    • General Math
Replies
4
Views
1K
MHB Help with Logarithms: Find 2^A
    • General Math
Replies
2
Views
1K
MHB How Can I Express a Combination of Logarithms as a Single Logarithm?
    • General Math
Replies
4
Views
2K
B How to check if this limit is correct or not?
    • General Math
Replies
5
Views
1K
Express logarithm in another variable
    • Precalculus Mathematics Homework Help
Replies
4
Views
1K
Find the Value of z in z^{1+i}=4 using Logarithms
    • Precalculus Mathematics Homework Help
Replies
1
Views
1K
MHB Calculating a Logarithmic Product Series
    • General Math
Replies
2
Views
2K
MHB Change of bases with log tables
    • General Math
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top