How To Change Base Of Log On Calculator
Log Reckoner
Anti-Log Estimator
| Number ∓ Base | Corporeality |
|---|---|
| Enter the number(to the power of 10) | |
| Select the Base value | |
| Antilog Result | Amount |
|---|---|
| Antilog value |
Mathematical Formulas
Calculating log (logbx):
logbx = y implies by = x.
Where,
- b = base,
- y = number,
- x = log value.
Calculating Antilog:
y = 1010
Where,
- x = number,
- y = antilog value.
Logarithms and Anti-Logarithms: How Information technology Works and Its Significance
- Guide Authored past Corin B. Arenas, published on October 1, 2019
If you've ever wondered how experts determine not bad distances, earthquake intensity, and global economical growth rates, and so you lot've come up to the correct place.
Calculating very large sums can be slow and confusing. Merely with the help of logarithms (log) and antilogarithms (antilog), calculations can be fabricated simpler.
Read on to learn more than about log and antilog, how they work, and why these are relevant mathematical concepts.
What is Logarithm?
A logarithm is the power to which a number (referred to every bit the base) must be multiplied to itself to obtain a given number. In simpler terms, logarithm solves the trouble:
How many times do we multiply b to obtain another number y?
Logarithm counts the number of times the same factor must exist multiplied to make it at a given number.
Who Came Up with It?
Log was invented in the 16th century equally a calculation tool by Scottish mathematician, physicist and astronomer, John Napier. He wrote the volume Mirifici Logarithmorum Canonis Descriptio with tables and numbers discussing natural logarithms, laying downward the groundwork for its basic concept.
Napier coined the term logarithm from the Greek give-and-take logos which means 'ratio or proportion,' and arithmos which means 'number.' When combined, it literally ways 'ratio number.'
ii Types of Logarithms
The natural logarithm of a number is its log to the base of the abiding e, where eastward is approximately equal to two.718281828459. The equation is written as log e (10).
If a logarithm does not specify a base, like this example: log(grand), it's known every bit a common logarithm that uses the base 10.
log(thousand), it's known as a common logarithm that uses the base ten.
How is Log Used?
Once you showtime computing figures by millions, billions and trillions, it can go quite taxing. Whether it concerns counting a lot of coin, the growth of populations, or covering large distances, log can piece of work for you. It can simplify large sums that involve long and confusing equations, making them easier to grasp.
Here is the standard equation for log:
logb(x) = y
Where,
- The number multiplied to itself (b) is the base.
- The number of times it is multiplied (y) is the logarithm.
- The number obtained (x) is written in the parenthesis.
To understand how the concept works, hither'due south an example with a smaller number:
Question: How many 2s do we multiply to get 32?
b = ii, ten = 32
log2(32) = y
Answer: 2 x two x 2 x ii x 2 = 32
v number 2s must be multiplied to obtain the number 32.
The answer: log2(32) = 5
Therefore, in this example: The logarithm of 32 with base two is 5, or log base two of 32 is 5.
Moreover, log is the inverse function of exponentiation, where the mathematical operation is written equally bn. b is the base that is multiplied according to the power of n, which is the number of times it is multiplied to itself.
What does this mean? The log of a number is the exponent to which base of operations b is multiplied to obtain a given number. To give you a amend thought, refer to the sample log equation set alongside its exponential equation below.
| log | exponent |
|---|---|
| log2(32) = 5 | 25 = 32 |
Now let'south endeavour it with a large number.
Question: How many 10s do we multiply to become 150,000,000,000?
b = x, x = 150,000,000,000
logb(10) = y
log(150,000,000,000) = y
y = 11.1760912590557
log(150,000,000,000) = eleven.1760912590557
This is solved by using the log function in a scientific reckoner. Or use the estimator on this page to go the respond.
How is Antilogarithm Related to Log?
A log number tin then exist returned to its original number. This can exist done using antilogarithm (antilog). Thus, the antilog is the inverse function of log. Too, antilog functions to exponentiate a simplified log value.
To compute the antilog of a number y, you lot must raise the logarithm base b (usually 10, sometimes the constant e) to the power that will generate the number y.
Here is the equation for antilog using base of operations 10:
1010 = y
Where 10 is the exponent and y is the antilog value.
For instance, if we take this equation, log(5) = x, its antilog will be 10x = 5.
- Log: log(v) = 0.698970004336019
- Antilog: 100.698970004336019 = 5
Now permit's effort it with a larger number.
If we take log(150,000,000,000) = x, its antilog volition be 10x = 150,000,000,000.
- Log: log10(150,000,000,000) = 11.1760912590557
- Antilog: 10xi.1760912590557= 150,000,000,000
Importance and Real-World Applications
Prior to the invention of calculators, logarithms were used to simplify computations in various fields of knowledge, such as navigation, surveying, astronomy, and afterward on, engineering.
Imagine sailing in the middle of nowhere in the 16th century. Navigators back and then relied on the position of stars and a sextant mechanism to pinpoint their exact location. Without modernistic technology to help you compute great distances, you tin can use log to simplify your calculations. Accuracy is important, or you risk more days at sea with meager supplies. Fewer equations mean less room for fault.
What about other practical applications? Live Scientific discipline states logarithms relate geometric progressions to arithmetic progressions. If you've ever noticed repetitive shapes and patterns in nature, architecture, and art, these formations possess their own corresponding logarithmic values.
Today, noesis from how these patterns work influences the way humanity constructs and designs houses, buildings, and urban landscapes.
Logarithms are also used to express the extent and intensity of certain scales. Autonomously from wide distances, and high speeds, it measures other things such equally:
- Sound intensity
- Sound frequency
- Force of windstorms
- Strength of earthquakes
- Corrosive level of acids
- Hardness of minerals
- Brightness of stars
Let'southward take decibels every bit an example. To make speakers louder by 10 decibels, it must be supplied past 10 times the power. As y'all increase it to +20 dB, it will need 100 times the power, and by +thirty dB it will need 1,000 the power.
Moreover, sound intensity progresses arithmetically. It also changes proportionally with the logarithm of a sound moving ridge which progresses geometrically.
Below is a table from Live Science list different logarithmic scales with their corresponding linear scales.
| Field of Measurement | Linear Calibration | Logarithmic Scale |
|---|---|---|
| Sound Intensity | Power (×10) | Decibels (dB) (+10) |
| Annotation Pitch | Frequency (×two) | Note (+12 half steps) |
| Effulgence of Star | Power per unit expanse (×100) | Magnitude (-5) |
| Earthquake Intensity | Energy (×chiliad) | Richter Scale (+2) |
| Air current Intensity | Current of air speed (×1.5) | Beaufort Scale (+ane) |
| Mineral Hardness | Absolute hardness (×3 approx.) | Mohs Calibration (+1) |
| Acerbity or Basicity | Concentration of H+ions (×10) | pH (-one) |
In Measuring Rates and Ranks
According to Kalid Azad, the math educator backside BetterExplained.com, logarithms are how we figure out how fast something is growing.
Common logarithms basically describe numbers in terms of their powers of 10. When it comes to interest charge per unit, the logarithm is the growth in an investment.
In determining the Gdp growth rate of a country, analysts review Gross domestic product in subsequent years. They take the Gross domestic product of the previous year, and the Gross domestic product the following year, and so compute the logarithm to find the estimated growth rate.
Search engines employ the link graph to help score the importance, trustworthiness & authorization of documents across the web. Google's PageRank was a major evolution in search which boosted search relevancy and helped Google search marketshare.
Co-ordinate to Azad, in a scale of 1 to 10, a landing page with a PageRank of ii is 10 times more pop than a page with a PageRank of ane. If a site has a PageRank of 5, and a competitor site has a PageRank of nine, then it has a difference of 4 orders of magnitude.
An order of magnitude ways roughly a 10x deviation, or a ranking is 1 digit larger compared to the other. In this instance, a site with a PageRank nine is 100,000,000 more than popular than a site with PageRank 1.
The Bottom Line
Log and antilog are meaning calculating methods that allow us to simplify big sums. Simplifying shortens the computation procedure and makes calculations easier to grasp. This helps reduce room for error.
Moreover, using log provides measurable scales for gauging natural phenomenon, similar earthquake intensity, the strength of windstorms, and the brightness of stars. In terms of finance, logarithms allow us to pinpoint interest rates and economical growth rates.
It'south practically used in many fields. Large values that depend on the accuracy of measurement benefit from using logarithmic calculations.
Nearly the Author
Corin is an agog researcher and writer of financial topics—studying economical trends, how they affect populations, also as how to help consumers brand wiser fiscal decisions. Her other feature articles can exist read on Inquirer.cyberspace and Manileno.com. She holds a Master's caste in Creative Writing from the University of the Philippines, one of the meridian academic institutions in the world, and a Bachelor'due south in Communication Arts from Miriam Higher.
Source: https://www.calculators.org/math/log-antilog.php
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