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Can you multiply two irrational logarithms to get a rational answer?
Yes. Take any rational number p. Let a = any number that is not a power of 10, so that log(a) is irrational. and let b = p/log(a). log(a) is irrational so 1/log(a) must be irrational. That is, both log(a) and log(b) are irrational. But log(a)*log(b) = log(a)*[p/log(a)] = p which is rational. In the above case all logs are to base 10, but any other base can be used.
How do you put log functions in a TI-84?
In order to find the log with a power of ten, use the LOG button. For example, to find log105, type log(5). (The parenthesis after the g will appear when you press the LOG button. In order to find a log with a power other than ten, you will have to divide by the log10 of that power. For example, to find log82, type log(8)/log(2). In order to find the natural log of a number, use the LN key. For example, to find the natural log of 91, type ln(91).
Log -3 equals?
There is no answer - it is an error: negative numbers do not have logarithms. The log if a number tells to what power the (positive) base must be raised to get the number. Raising any positive number to any power will never result in a negative number, so it is an error to try and take the log of a negative number.
How do you find the number of years it takes to double a principle on compound interest?
If you have studied logarithms, the answer is simple: The number of years = log(2)/log(1 + r/100) where the annual rate of interest is r%. The logs can be to any base: 10 or e (or any other base). The number of years for it to treble is log(3)/log(1 + r/100) and so on. Without logs, it is a question of trial and error. 100/r year WILL be too large.
Do all logarithms require a base of 10?
No. The so-called "natural" logarithms have a base of ' e ', and you can find the log of any positive number to any base you like.
What is the anti-log of 12.34?
The anti-log of 12.34 is the inverse operation of taking the logarithm of a number. In this case, the anti-log of 12.34 is equal to 10^12.34, which is approximately 2511886431. A logarithm is the power to which a base must be raised to produce a given number, so the anti-log reverses this operation to find the original number.
How do you find log of a number using log tables?
what if I give you the wrong answer
How do you use the anti log on a TI-89 calculator'?
To find anti log of a number enter the number as the exponent of 10.
How do I solve the equation e to the power of x equals 2 using logarithms?
When the logarithm is taken of any number to a power the result is that power times the log of the number; so taking logs of both sides gives: e^x = 2 → log(e^x) = log 2 → x log e = log 2 Dividing both sides by log e gives: x = (log 2)/(log e) The value of the logarithm of the base when taken to that base is 1. The logarithms can be taken to any base you like, however, if the base is e (natural logs, written as ln), then ln e = 1 which gives x = (ln 2)/1 = ln 2 This is in fact the definition of a logarithm: the logarithm to a specific base of a number is the power of the base which equals that number. In this case ln 2 is the number x such that e^x = 2. ---------------------------------------------------- This also means that you can calculate logs to any base if you can find logs to a specific base: log (b^x) = y → x log b = log y → x = (log y)/(log b) In other words, the log of a number to a given base, is the log of that number using any [second] base you like divided by the log of the base to the same [second] base. eg log₂ 8 = ln 8 / ln 2 = 2.7094... / 0.6931... = 3 since log₂ 8 = 3 it means 2³ = 8 (which is true).
How do you use logarithm tables for division?
Suppose you want to divide x by y Find log(x) and log(y) to any base b (usually 10 or e) Calculate z = log(x) - log(y) Look up the antilog of z (or find the number whose log is z). x/y = antilog(z)
What is a number for which a given logarithm stands?
A number for which a given logarithm stands is the result that the logarithm function yields when applied to a specific base and value. For example, in the equation log(base 2) 8 = 3, the number for which the logarithm stands is 8.
Can you multiply two irrational logarithms to get a rational answer?
Yes. Take any rational number p. Let a = any number that is not a power of 10, so that log(a) is irrational. and let b = p/log(a). log(a) is irrational so 1/log(a) must be irrational. That is, both log(a) and log(b) are irrational. But log(a)*log(b) = log(a)*[p/log(a)] = p which is rational. In the above case all logs are to base 10, but any other base can be used.
How do you put log functions in a TI-84?
In order to find the log with a power of ten, use the LOG button. For example, to find log105, type log(5). (The parenthesis after the g will appear when you press the LOG button. In order to find a log with a power other than ten, you will have to divide by the log10 of that power. For example, to find log82, type log(8)/log(2). In order to find the natural log of a number, use the LN key. For example, to find the natural log of 91, type ln(91).
Log -3 equals?
There is no answer - it is an error: negative numbers do not have logarithms. The log if a number tells to what power the (positive) base must be raised to get the number. Raising any positive number to any power will never result in a negative number, so it is an error to try and take the log of a negative number.
What are the steps involved in multiplication using logarithms?
Given X and Y, you wish to find X*Y using logarithms.Find a = log(X) and b = log(Y) to any base zCalculate c = a + bFind z^c: this is the required answer.You can take logs to any base, z. For common logs, the base is 10; for natural logs it is e (Euler's number).
How do you find the number of years it takes to double a principle on compound interest?
If you have studied logarithms, the answer is simple: The number of years = log(2)/log(1 + r/100) where the annual rate of interest is r%. The logs can be to any base: 10 or e (or any other base). The number of years for it to treble is log(3)/log(1 + r/100) and so on. Without logs, it is a question of trial and error. 100/r year WILL be too large.
Do all logarithms require a base of 10?
No. The so-called "natural" logarithms have a base of ' e ', and you can find the log of any positive number to any base you like.
