Value of Log e

Value of log e is 0.434294481. There are two values of log e, first is log e base e which is equal to 1, and second is log e base 10 which is equal to 0.434294481. Log e is made up of two terms Log and e where Log is a logarithm function, where one number is raised on the power of another number to calculate mathematical expression and e is an irrational constant also known as an exponential constant.

In this article, we are going to learn what is the value of log e, how the value of log e is derived, and how to calculate the value of log e.

What is the Value of Log e?

Log e can be calculated in two different cases. One is finding the natural logarithmic value and the other is the common logarithmic value. The two types of Value of Log e are discussed below:

Value of log e base e

Value of log e using natural logarithm is unity i.e., equal to 1. Log x is a natural logarithm and it has a base equal to e. So, Log x is equal to the value Log_e x and hence the value of log e can be written as log_e e. Now the base value is equal to the index value so, the value of the logarithm function is 1. Hence the value of log e is equal to 1.

log_ee = 1

Value of log e base 10

Value of log e is equal to 0.434294481 when log e has a base equal to 10. Common logarithm is said when log e to the base is equal to 10. Common logarithm of any value is calculated by dividing the value of its natural logarithm by 2.303 because the value of log10e is equal to 2.303

log₁₀e = 0.434

What is e?

e is Euler’s Number which is an irrational mathematical constant. The value of e is equal to 2.71828182845904………..so on. The value of e was calculated by mathematician Jacob Bernoulli. The value of e is used in various mathematical fields such as calculus, derangement, compound interest, probability, exponential function, and many more.

How to Derive the Value of Log e?

Let’s see how to calculate the value of log to the base 10

Using Log Formula

log_ba = log_ca/log_cb

log₁₀e = (log_ee) / (log_e10)

⇒ log₁₀e = 1/ log_e10

⇒ log₁₀e = 1/2.302585

⇒ log₁₀e = 0.434294481

Hence, log10e = 0.434(approx.)

We can also derive the value of log₁₀e in the following manner:

log₁₀e = log₁₀(2.71828) = 0.4342944

Learn More, Log Table

Derivative of Log e

The value of log e at both bases i.e. 10 and e is a constant value. The value of log e at base e is 1 and the value of log e at base 10 is 0.434 approximately. Hence, in both cases we get a constant value and we know that the derivative of a constant is zero. Hence, the derivative of log e is zero. This can be given as follows

• d/dx(log_ee) = d/dx(1) = 0
• d/dx(log₁₀e) = d/dx(0.434) = 0

Learn More, Derivative of Logarithmic Function

Points to Remember about Log e

• The value of log_ee is equal to 1 .
• The value of log₁₀e is equal to 0.4342944
• Natural logarithm of infinity is infinity.
• Natural logarithm of -1 is constant.
• Natural logarithm of √e is equal to 1/2.

Practice Problems Related to Value of Log e

Example 1: Find the Derivative of log_ee

Solution:

We know that log_ee = 1

Hence, d/dx(log_ee) = d/dx(1) = 0

Example 2: What is the value of log₅ 125?

Solution:

log₅125 = log₅(5)³

Using Log Formula

log₅(5)³ = 3log₅(5) = 3 × 1 = 3

Example 3: What is the value of p in log₅ (p-2) = 1 ?

Solution:

log₅(p-2) = 1

⇒ 5¹ = p-2

⇒ 5 = p-2

⇒ p = 5 + 2 = 7

Practice Questions on Value of Log e

Q1: If e^x = 5.5, Find x.

Q2: Given that log_e(x – 2) = 6, find x.

Q3: Find the value of √e.

FAQs on Log e

1. What is Logarithm Function?

Logarithm function is inverse of exponential function. It can be represented as f(x) = Log_a x , where a > 0 .

2. What is the value of log_ee?

Value of log_e e is equal to 1

3. What is the value of log_e 10?

Value of log_e 10 is equal to 0.43429.

4. What is the Value of Constant e?

Value of e is 2.71828182845904…….

5. What is the formula of ln(p.q)?

ln(p.q) = ln (p) + ln (q)

6. What is the value of Derivative of log e?

Derivative of log e is equal to zero.

7. What is the Formula of ln(x/y)?

ln(x/y) = ln(x) – ln(y)

8. What is Natural Logarithm of Infinity?

Natural logarithm of infinity is infinity