Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

What is log5 ? How can we find logs of numbers without using a calculator?

Answer
VerifiedVerified
421.8k+ views
1 likes
like imagedislike image
Hint: Logs (or) logarithms are nothing but another way of expressing exponents. We will use the log tables to find the value of log5 , and for that we need to use the logarithm identities. Here we will use the division rule: log (a/b) = log a – log b. Then, find the values from the log table and calculate using a calculator we will get the final output. Next, we will show how to find the value of log5 without using a calculator.

Complete step-by-step answer:
Simplest way is to calculate log5 by referring to logarithmic tables, which shows log5=0.6990.
Another way could be using log2=0.3010 and log10=1 (again for this we need log tables).
Suppose we need to find the value of log5:
Here, we will use the logarithm identity: log(ab)=logalogb
So, log5 can be expressed as
log5=log(102)
=log10log2
Substituting the values of log, we will get,
=10.3010
=0.6990
Hence log5=0.6990.
Next, we will find the value without using the calculators:
It is often needed to get the logarithm of a number without log tables.
So, it is good to know of the techniques which will be useful in finding the logarithm of many numbers.
Let us see how to find logarithmic values without the use of a calculator.
In a common logarithmic function, the base of the logarithmic function is 10. i.e. log10or log represents this function. And in natural logarithmic function, the base of the logarithmic function is e. i.e. logeor ln represents this function.
In fact one needs to remember log (to the base 10) for the first ten numbers and it makes things a lot easier.
log1=0
log10=1
Also, we also know that
log2=0.3010
log3=0.4771
log7=0.8451
loge=0.693
Learn the above logarithms, as they will be useful in solving the logarithm of other numbers that are frequently required in various exams.
Then all logs can be worked out using these as
log4=2log2
log5=1log2
log6=log2+log3
log8=3log2
log9=2log3
In this way, we can find the other logarithmic values.
Using this technique, it is easy to find the logarithm of large numbers. But there are some numbers for which we cannot use this method. For example log11.

Note: A logarithm is defined as the power to which number must be raised to get some other values. It is the most convenient way to express large numbers. There are three logarithm identities which one should know. They are:
1) Product rule: log (ab) = log a + log b
2) Quotient rule: log (a/b) = lag a – log b
3) Power rule: log (a^b) = bloga
Logarithms are also said to be the inverse process of exponential. The basic advantage of using logarithm base 10 is that they are easy to compute mentally for some special values. Natural logs are easier to use for theoretical work. They are easy to calculate numerically.