Logarithm contributes in advance science and astronomy as it helps in surveying, celestial navigation and other domains. Pierre Simon Laplace called logarithm. Tables of logarithms enable it for practical use.
What is Logarithm?
The logarithm is the inverse of the exponent function. By inverse, it means a function that does the opposite of the exponent function.
Consider an examples like subtraction is the inverse of addition and division is the inverse of multiplication. Where exponent means to multiply a number "x" times like 2x and multiply them together.
Log Function using actual numbers
Logarithm identify the ways to repeatedly multiply the base for getting number. For example, log2 (x) counts how many 2s would need to be multiplied to make x.
24 = 16
Log2 (16) = 4
Both deals with this series of multiplication 2x2x2x2
The exponent takes the count and multiples to make a number. Logarithms take the final number and determine the count of multiplication. The log function is all about repetition of numbers.
Common Factors in Exponents and Logarithms
Exponents and logarithms deal with the "base". The "base" of the exponent is same as the base of the logarithm. Base is vertically the lowest number to write in both cases.
Such as 4x and log4 (x) are both base 4 and these bases are directly connected
If 4x = y then log4 (y) = x
Logarithm rules determines the relationship between natural log and exponential function.
S eln c = c ...... 1
By combining the values of "c", we get
Ln (ek) = k ..... 2
These equations explains that ex and lnx are inverse functions. Let's drive the rules of logarithms based on equation.
Rule #1: Product Rule
ln (xy) = ln(x)+ln(y)
Rule #2: Quotient Rule
ln (x/y) = ln(x)−ln(y)
Rule #3: Log of Power
ln (xy) = yln(x)
Rule #4: Log of e
ln (e) = 1
Rule #5: Log of One
ln (1) = 0
Rule #6: Log of Reciprocal
ln (1/x) = − ln(x)
Applications of Logarithms
Logarithm applications can be found inside and outside the mathematics. The logarithms are used in
- Logarithmic Scale
- 2 Digit Expense Calculation
- Finding Order of Magnitude
- Calculating Interest Rates
- Logarithmic Graphs
For calculating inverse or antilogarithm, use our antilog calculator for free.
What is a Log Calculator?
Just like other math concepts, calculations of logarithm needs time and practice. Calculatored has developed this log calculator which is fast, accurate and free to use. The natural logarithm calculator helps you finding logs of different numbers.
How to use Log Calculator?
The log calculator is very simple and easy to use. You don't need to be a master to use it. Follow below steps to get log value of your desired digits
Step #1: Enter numeric values in Log calculator.
Step #2: Select between the base of 2, e and 10.
Step #3: Click on the "CALCULATE" button.
You will get the results right after clicking on the calculate button. This makes our log calculator also one of the fastest among those you find online.