Logarithms, the inverse equation of an exponent, can be useful in rationalizing many quantities in science, mathematics, and even finance. With logarithms, you can simplify complicated numbers and make them much easier to understand. By inputting your variables into the log calculator, you can quickly rationalize any number of very large or small magnitude. For your calculations, you can use natural logarithms, common logarithms, or any base of your choosing.
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What is a logarithm?
The idea of
(log) is to identify what exponent is needed for one number to become another. Log counts the number of multiplications that are added to the base number, and by tallying the factors of multiplication, you can determine log. However, using the log operation can help you to solve for the answer much more efficiently.
The understanding of log is relevant in many aspects of science, engineering, math, and computer science, and can even be used in finance when assessing
and investment returns. Logarithms, in the simplest explanation, find the cause for an effect or the input required to achieve an output.
Working with large numbers can be difficult. It can be easy to miss a digit and skew the value, while multiplying large numbers can become increasingly involved. Log provides a means to simplify large numbers into exponential values for financial calculations and scientific measures. By writing numbers concerning their inputs, they become much easier to understand.
Using the common logarithm base of 10, we can simplify the following numbers and quantities:
One thousand = 10^3
One million = 10^6
The number of protein molecules in a single cell = 10^7
One billion = 10^9
The average weight of a star in grams = 10^35
Approximate number of molecules in the known universe = 10^80
Using the log values of these figures can ensure that there are no errors in accuracy when explaining these terms and prevent any mistakes from being made when using these numbers in other mathematical formulations.
Properties of log
When stripped down, log answers the question of how many of one number you need to multiply to get another number. For example, how many 2s do you multiply to get 16?
2 x 2 x 2 x 2 = 16
You have to multiply four of the
Therefore, the logarithm is
You can write out the question, how many 2s do you need to multiply to get 16, in a logarithm equation:
Which says the following:
The number being multiplied, (2), is the base so the following can be said:
• The logarithm of 16 with a base of 2 is 4.
• Log base 2 of 16 is 4.
• The base-2 of log 16 is 4.
When working out a logarithm, you are dealing with three different numbers:
• The base, which is the starting number.
• The logarithm, which is how many times you have to increase the base number – the 4 the example above.
• The numeral, which you are trying to multiply to get and is always in brackets – the (16) in the example above.
Solving for log
Log is the inverse calculation of an
, meaning log will answer how many times a number is used in multiplication. Therefore, it can respond to the following question:
In the following way:
The logarithm tells us that the exponent is 4. Using this computation, you can come up with a general formula to solve for different log variables:
Using the logarithm calculator you can quickly check your work as you complete the log equations. Even though you can use any number as a log base, certain base formats are used more universally in some areas of study.
Common logarithms are used mostly in engineering and general sciences and use a base of 10. In some instances, it is possible to see log written without a base, which implies that the base is actually 10.
log(1000) = log10(1000)
log10(1000) = 3
Natural logarithms differ from common logarithms in that they use a base of e (2.71828), which is a famous irrational number and has tremendous significance for mathematicians. By replacing log with ln, you can also condense natural logarithms.
ln(7.389) = log e(7.389)
log e(7.389) ≈ 2
How to use the calculator
The logarithm calculator is very easy to use and is divided into two parts: a data section and a results section. To get accurate results, you must include some values relative to the equation. Let’s review this together.
Initially you should specify the base of the logarithm by selecting an option between e, 2, 10, or other. If you choose other, you may add a value in this space by using the arrows or your keyboard.
Then, on the first line of the calculator you may identify the final numeral you want to use in the equation.
Click on the ‘calculate’ button to get your report. Your results will be divided into two formats using the log formula and the exponential equivalent as proof.
Add, subtract, multiply, or divide logarithms
It is possible to add, subtract, multiply, and divide logarithms by exploring different formulations. When the subject of log is the
of two numerals, the log can be reformatted by the
of the numerals:
When the log is a
of two numerals, it can be rewritten in
Logarithms can be useful in any instance you would like to rationalize numbers of very high and small magnitudes better. In life, interest is compounded by using
and understanding the math can be a great asset when comes to interpreting loans and
. Meanwhile, working out how to take your
can come down to simple logarithmic equations. Don’t take a chance with the computations and always use a calculator to verify your work.
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