Understanding Logarithms?
First, logarithms are not birth control methods used by lumberjacks (um, old math joke... sorry about that...) IMO, logarithms are most useful when you are dealing with large numbers. For example, if you need to know about how big 2^100 is, you could spend all day calculating it, or you could do a logarithmic calculation that takes a few minutes: log 2 = .30103, therefore log 2^100 = 30.103, so 2^100 is a somewhat more than 10^30. The point to logarithms is that you are dealing with exponents, i.e. log 2 = .30103 means 10^.30103 = 2. So, to multiple two numbers, you add their exponents, while to find the power of a number, you multply the logarithm by the power. (This may sound like Greek right now, but it will make sense when you understand logarithms better.) I guess it should also be mentioned (as ocdscale does) that certain types of measurements are done on a logarithmic scale because they make more sense. For example, the Richter scale used to measure earthquakes is a logarithmic scale.
Which book is good for Logarithm in IITJEE?
Hello Buddy!!!For good practice in logarithms you should start with G.TEWANI logarithm followed by past years papers and also questions from coaching materials(you can also practice from R.D Sharma OLD edition)…That would be enough!!!Hope it helps..☺
What are logarithms used for? Are decibels a good example of the usefulness of a logarithm? Are logarithms calculus?
2 is twice as big as 1. And 4 is twice as big as 2. And 8 is twice as big as 4. But the gap between 1 and 2 is not the same as the gap between 2 and 4. And both of these are smaller than the gap between 4 and 8.Logarithms are a way of showing how big a number is in terms of how many times you have to multiply a certain number (called the base) to get it. If you are using 2 as your base, then a logarithm means "how many times do I have to multiply 2 to get to this number?".Since 2 * 2 = 4, the logarithm of 4 is 2. Since 2 * 2 * 2 = 8, the logarithm of 8 is 3 (assuming you are using 2 as your base. Really you can use any number you want. The most common numbers to use are 2, 10, and 2.71828).Logarithms are useful because they are the way our brain naturally understands most things. If there are two similar items that cost $2 and $4, then the $4 is a lot more expensive than the $2 item. You would probably buy the $2 item. If you have two items that cost $100 and $102, then the difference isn't much, and you might buy the more expensive one. The gap between these two is the same, but you have to multiply 2 once to get to 2, and twice to get to 4 - that's a whole extra two! .You have to multiply two 6.6 times to get to 100, and 6.7 times to get to 102 - that's a difference of only 0.1 twos when you think in logarithms.
Which of the following cannot be a base for exponential and logarithmic functions?
all of them could, although if you use 1 its just the boring function f(x) = 1, so that's prolly the one they want you to pick, if any
How do I solve the logarithmic equation.
I think this is what you mean (where I am using log7 to mean log to the base 7). Just read your additional comments so here is my new answer: log7(x) + log7 (x - 48) = 2 Use the fact that: log7(a) + log7(b) = log(ab) log7[x(x - 48)] = 2 Now use the fact that: log7(a) = b can be changed to a = 7^b x(x - 48) = 7^2 = 49 x^2 - 48x - 49 = 0 (x - 49)(x + 1) = 0 The answers are: x = 49 and x = -1 However x = -1 is not a good solution since x > 48 based on the second term of the original equation. Since we are taking log7 of (x - 48) x must be greater than 48 to get a valid log. The answer is x = 49 Check: log7(49) + log7(49 - 48) = log7(49) + log7(1) = 2 + 0 = 2 And the answer given above is correct
Olve for x using logarithms. Give an exact answer. Do not enter a decimal approximation. 4x(2^x) = 9x(6^x)?
4x(2^x) = 9x(6^x) 4x(2^x) = 9x(3^x)(2^x) 4x(2^x) - 9x(3^x)(2^x) = 0 x 2^x(4 - 9(3^x)) = 0 x = 0 or 2^x = 0 or 4 - 9(3^x) = 0 Discard 2^x = 0 because it has no solutions, leaving just x = 0 or 4 - 9(3^x) = 0 x = 0 or 4 = 9(3^x) x = 0 or 4/9 = 3^x x = 0 or ln(4/9) = ln(3^x) x = 0 or ln(4/9) = xln3 x = 0 or ln(4/9)/ln3 = x
How can I master myself in logarithm?
I did it this way:Write about it. Try to define logarithm by yourself (In a way you understand it) - do this enough times and you will be more and more familiar with the concept. Write examples of logarithm - your own ones - even though they’re easy. My experience is, if you make examples of a concept by yourself, you understand it better.The next step is memorizing important properties of logarithm, they are farily easy to prove, all the proofs use the same concept - log is the inverse of exponentiation - if you are interested then search for the proofs - otherwise memorize them (I strongly recommend to at least go through and understand all the proofs - they are essential for your understanding):[math]log_a {mn} = log_a m + log_a n[/math][math]log_a b^n = n*log_a b[/math][math]log_a b = \frac{1}{log_b a}[/math][math]log_a a = 1[/math][math]log_a a^n = n[/math][math]log_a \frac{m}{n} = log_a m - log_a n[/math] (can be proved by combining property 1) and 2)[math]log_a b = \frac{log_x b}{log_x a}[/math] This is quite interesting and useful also. Here, x can be any base8. [math]log_a 1 = 0[/math]9. [math]log_{a^n} b = \frac{1}{n} log_a b[/math] and as a result, [math]log_{a^n} b^m = \frac{m}{n} log_a b[/math]The third step is to practice : This is fairly obvious. You have to also study examples and note some patterns. You may have a question like :[math]log_{10} 2 = 0.301[/math]. Then [math]log_{10} 5[/math] = ?Using property 1,[math]log_{10} 10 = log_{10} 5 + log_{10} 2[/math]. 10 = 5 x 2[math]1 = log_{10} 5 + 0.301[/math].[math]log_{10} 5 = 1 - 0.301 = 0.699 .[/math]Another example:[math]log_e 8 = m[/math], [math]log_e 2 = n[/math]. Then [math]\frac{m}{n}=[/math] ?Solution:[math]\frac{log_e 8}{log_e 2} = log_{2} 8[/math] ( Property (7))So, [math]\frac{m}{n} = log_{2} 2^3[/math]. 8=[math]2^3[/math].So, [math]\frac{m}{n} = 3.[/math] (Property (5))The more patterns you notice the easier it gets. The property 1,2,5 and 7 are most used but you should memorize all of the 9. As a practice, you may attempt to prove them by yourself.(Last Edited : 5 December 2018)
Can someone help me create a poem about Logarithms?
Use the following for ideas and inspiration to get you started:- Poems about Logarithms http://allpoetry.com/poem/628702-logarit... This is a great site http://www.totopoetry.com/search.asp?wor... Lady Logarithm -- A Mathematical Love Poem http://www.youtube.com/watch?v=x6OYDktVb... -
Is logarithm a hard part of mathematics?
No.I’ve never understood why people think logarithms are hard; it's very common for people to feel uncomfortable with them. Trigonometric functions are harder to deal with but people tend to be more comfortable with them than logarithms. I think it's just a lack of exposure in earlier math classes compared to functions like polynomials and trig functions.Logarithms are the inverse functions to exponential functions. There are some very nice properties that logarithms have, the basic of which are listed here:Mathwords: Logarithm Rules