Binary Logarithm,Natural Logarithm,Common Logarithm,Anti-Logarithm Calculation
Logarithm Calculator
An online complete log logarithm calculator.
Logarithm is the inverse function to exponentiation.
First, we see about exponentiation,
Exponentiation is an expression that involves two numbers, a base and an exponent, where an exponent is mathematical shorthand representing how many times a number is multiplied against itself.
Example
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
25 = 64
with same above entries, Now we see about Logarithm, i.e Inverse function to exponentiation
log2 2 = 1
log2 4 = 2
log2 8 = 3
log2 16 = 4
log2 32 = 5
log2 64 = 6
Logarithm Formulas Used In Our Calculators
1. Log Formula
logb(x) = y
x = logb(bx)
logb(x) = y is equivalent to x = by
(logb(x) => This read as log base b of x is equals to y )
b: log base number, b>0 and b≠1
x: is real number, x>0
2. Natural Logarithm or Logarithm Base e Formula
Log base e is also called as natural logarithm.
Natural logarithm symbol is ln.
ln(x) = y
ln(x) is equivalent to loge(x)
x: is real number, x > 0
3. Common Logarithm or Logarithm Base 10 Formula
Log base 10 is also called as common logarithm.
log10(x) = y is equivalent to x = 10y
log10(x) = log(x)
x: is real number, x>0
4. Binary Logarithm or Logarithm Base 2 Formula
Log base 2 is also called as binary logarithm.
log2(x) = y is equivalent to x = 2y
x: is real number, x>0
5. Antilogarithm (or Inverse logarithm) Formula
Calculate the inverse logarithm of a number.
When
y = logb x
The anti-logarithm is calculated by raising the base b to the logarithm y
x = logb-1(y) = b y
List Of Logarithmic Laws or Rules or Identities
Important formulas, sometimes called logarithmic identities or logarithmic laws.They are
Logarithm of a Product
logb (xy) = logb x + logb y
Example
log3 243 = log3 (9 . 27) = log3 9 + log3 27 = 2 + 3 = 5
Logarithm of a Quotient
logb (x/y) = logb x - logb y
Example
log2 16 = log2 (64/4) = log2 64 - log2 4 = 6 - 2 = 4
Logarithm of a Power
logb (xp) = p logb x
The logarithm of an power number where its base is the same as the base of the log equals the power.
Example
log2 64 = log2 (26) = 6 log2 2 = 6
Logarithm of a Root
logb p√x = (logb x) / p
Example
log10 √1000 = (1 / 2) . log10 1000 = 3 / 2 = 1.5
Logarithm of Zero
logb (1) = 0
The logarithm of 1 with b > 1 equals zero.
Logarithm of Identity
logb (b) = 1
The logarithm of a number that is equal to its base is just 1.
Logarithm of Exponent
blogb (k) = k
Raising the logarithm of a number by its base equals the number.
Change of Base
logb (x) = (logk (x)) / (logk (b))
Common Values for Log Base b
Base b | Name for logbx | ISO notation | Other notations |
---|---|---|---|
2 | Binary logarithm | lb x | ld x, log x, lg x, log2x |
e | Natural logarithm | ln x | log x |
10 | Common logarithm | lg x | log x, log10x |
Logarithm Values Tables
logb(x) = y |
---|
log2 (1) = 0 |
log2 (2) = 1 |
log2 (3) = 1.584962501 |
log2 (4) = 2 |
log2 (5) = 2.321928095 |
log2 (6) = 2.584962501 |
log2 (7) = 2.807354922 |
log2 (8) = 3 |
log2 (9) = 3.169925001 |
log2 (10) = 3.321928095 |
log2 (11) = 3.459431619 |
log2 (12) = 3.584962501 |
log2 (13) = 3.700439718 |
log2 (14) = 3.807354922 |
log2 (15) = 3.906890596 |
log2 (16) = 4 |
log2 (17) = 4.087462841 |
log2 (18) = 4.169925001 |
log2 (19) = 4.247927513 |
log2 (20) = 4.321928095 |
log2 (21) = 4.392317423 |
log2 (22) = 4.459431619 |
log2 (23) = 4.523561956 |
log2 (24) = 4.584962501 |
log2 (25) = 4.64385619 |
log2 (26) = 4.700439718 |
log2 (27) = 4.754887502 |
log2 (28) = 4.807354922 |
log2 (29) = 4.857980995 |
log2 (30) = 4.906890596 |
log2 (31) = 4.95419631 |
log2 (32) = 5 |
log2 (33) = 5.044394119 |
log2 (34) = 5.087462841 |
log2 (35) = 5.129283017 |
log2 (36) = 5.169925001 |
log2 (37) = 5.209453366 |
log2 (38) = 5.247927513 |
log2 (39) = 5.285402219 |
log2 (40) = 5.321928095 |
log2 (41) = 5.357552005 |
log2 (42) = 5.392317423 |
log2 (43) = 5.426264755 |
log2 (44) = 5.459431619 |
log2 (45) = 5.491853096 |
log2 (46) = 5.523561956 |
log2 (47) = 5.554588852 |
log2 (48) = 5.584962501 |
log2 (49) = 5.614709844 |
log2 (50) = 5.64385619 |