Log Calculator (Logarithm)

Calculate logarithms by providing any two values to find the third

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Log Calculator (Logarithm)

Please provide any two values to calculate the third in the logarithm equation logbx = y. It can accept "e" as a base input.

📐 Logarithm Calculator

loge(100) = ?

Common bases: e (natural log), 10 (common log), 2 (binary log)

📊 Calculation Results

Answer
4.6051701859881
loge(100) = 4.6051701859881
Verification
e4.6051701859881 = 100

Calculation Steps

1. Given: loge(100) = ?
2. Using natural logarithm formula
3. ln(100) ≈ 4.6051701859881
4. Therefore: loge(100) = 4.6051701859881

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📚 What is Log?

The logarithm, or log, is the inverse of the mathematical operation of exponentiation. This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. Conventionally, log implies that base 10 is being used, though the base can technically be anything. When the base is e, ln is usually written, rather than loge. log2, the binary logarithm, is another base that is typically used with logarithms.

If x = by; then y = logbx; where b is the base

Each of the mentioned bases is typically used in different applications. Base 10 is commonly used in science and engineering, base e in math and physics, and base 2 in computer science.

Basic Log Rules

Product Rule:
logb(x × y) = logbx + logby
EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1
Quotient Rule:
logb(x / y) = logbx - logby
EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699
Power Rule:
logbxy = y × logbx
EX: log(26) = 6 × log(2) = 1.806

Important Values

logb(1) = 0
logb(b) = 1
logb(0) = undefined
ln(ex) = x

Change of Base Formula

It is also possible to change the base of the logarithm using the following rule:

logk(x)
logk(b)
= logb(x)
Example: log10(x) = log2(x) / log2(10)