Understanding Logarithms - Find log2, log2.0*10^24 and log5

• ayazabdul
In summary, the conversation is about finding the value of log 2, log 2.0*10^24, and log 5. The participants discuss using log rules for multiplication and division to solve the problem, with one person questioning the accuracy of the given value and another mentioning the use of a calculator or log tables.

ayazabdul

hello everybody,

Don't you use a calculator?

ayazabdul said:
hello everybody,

i'm guessing that this is a log base 10 question, and given log 2 relate it to the other two logs using the log rules for multiplication and division (5 being 10 divided by 2)

ok, can please anyone explain how log 2.0*10^24 is equal to 24.30

ayazabdul said:
ok, can please anyone explain how log 2.0*10^24 is equal to 24.30
i'm not going to do all the work, but

taking log 2 = 0.30 (all logs base 10)

use log [a*b]= log a + log b with a = 2 and b = 10^24

then use log[a^b] = b log a with a = 10 and b = 24

then log[10] = 1

As Kesh mentioned, use log rules for multiplication and division, do you know these ?

First of all, no one can "explain how log 2.0*10^24 is equal to 24.30" because it isn't! That is an approximate value, correct to only two decimal places.

Do you know the "log rules" Kesh and arunbg referred to: log(ab)= log(a)+ log(b) and log(ab)= b log(a) ? Apply those to log(2.0*1024) to get, first,
log 2+ log 1024. Then log 1024= 24 log(10). The log(10) should follow from the definition of "log". log(2) you either look up in a table of common logarithms or use a calculator.

1. What is the purpose of logarithms?

Logarithms are used to solve exponential equations and to convert between different forms of exponential notation. They also help to simplify calculations involving large numbers.

2. How do you find the logarithm of a number?

To find the logarithm of a number, you need to identify the base of the logarithm and the argument (the number inside the logarithm). Then, you can use a calculator or a logarithm table to find the value of the logarithm.

3. How do you calculate log2?

Log2 is the logarithm with a base of 2. To calculate log2, you can use a calculator or the logarithm formula, which is log2(x) = ln(x)/ln(2).

4. What is the value of log2.0*10^24?

The value of log2.0*10^24 is 24. This is because log2.0 is equal to 0 and log10 is equal to 1, so the final result is log2.0*10^24 = log2*10^24 = 1*24 = 24.

5. How do you calculate log5?

Log5 is the logarithm with a base of 5. To calculate log5, you can use a calculator or the logarithm formula, which is log5(x) = ln(x)/ln(5).