Value of log 5

Value of the log 5 is approximately 0.69897. The value of log 5 is calculated on two bases 10 and e. On base 10, the value of log 5 is 0.69897 and the value of log 5 on base e is equal to 1.6094.

In this article, we will learn what is the value of log 5 on different bases, what is their meaning, and how to calculate the value of log 5.

What is Value of Log 5?

Value of log 5 is the number which when raised to a power of 10 results in the number 5. This value is called a common logarithm. However, the value of log 5 is also calculated on base 'e' which means the number raised to the power of 'e' gives 5 as the result. Here, e is the Euler's Number whose value is equal to 2.7182818.....

This value of log 5 is calculated on two bases which are mentioned below:

• Value of log 5 base 10
• Value of log 5 base e

Let's learn them in detail.

Value of log 5 base 10

Log base 10 is also called common logarithm. The value of log 5 base 10 is given below:

log₁₀5 ≈ 0.69897

Value of log 5 base e

Log base e is also called Natural Logarithm. The value of log 5 base e is given below:

log_e5 = ln 5 ≈ 1.6094

The expression "log 5 base e" is not standard notation, as logarithms are typically denoted with base 10 (log) or base e (ln, natural logarithm). If you see "log 5 base e," it may imply a change of base from base 5 to base e. In this case, you can use the change of base formula:

log_ba = log_ca / log_ca

So, if you want to find log 5 base e, it would be equivalent to ln 5 / ln e, and since the natural logarithm of e is 1, the result is ln 5.

How to Calculate Value of log 5

Value of log 5 can be calculated using the following two methods:

• Value of Log 5 using Log Table
• Value of log 5 using Logarithmic Formulas

Let's learn them in detail

Calculating Value of log 5 using the Log Table

Follow the below mentioned steps to calculate value of log 5 using Log Table

1. Identify the Characteristics: Locate the logarithmic table and identify the columns for the integer part and decimal part of the logarithm.
2. Find the Integer Part: In the table, find the entry corresponding to the whole number part of log5, which is 0 in this case.
3. Find the Decimal Part: Locate the row that corresponds to the first two digits after the decimal point. For log5, it would be 69.
4. Interpolate for Precision: If your table does not have an exact match for the decimal part, interpolate between the closest values to refine the result. For example, if 0.69 and 0.70 are listed and your value is 0.6990, interpolate accordingly.
5. Combine Integer and Decimal Parts: Combine the integer and decimal parts to get the final logarithmic value. For log5, it would be approximately 0.6990.

Calculating Value of log 5 using the Logarithmic Formula

Log 5 can be calculated using log formulas in the following

log 5 = log(10/2)

= log 10 - log 2

Since log (A/B) = log A - log B

Substituting the values:

log 5 = 1-0.3010

log 5 = 0.6990

Related Reads,

• Logarithm
• Logarithm Formula
• Log Table

Value of Log 5 - Solved Examples

Some examples value of log 5 are,

Example 1: Evaluate log 5³

Solution:

log5 ≈ 0.69897

⇒ log 5³ = 3 log 5 = 3 × log 5 = 3 × 0.69897 = 2.09691

Example 2: If 10^x = 5, find the value of x.

Solution:

x = log₁₀5

x = log5/log10

x = 0.69897/1

x = 0.69897

Example 3: Solve for y in the equation 5^y=125

Solution:

y = log₅125

y = log125/log5

y = 2.09691/0/69897

y = 3

Example 4: If log₅x = 2, find the value of x.

Solution:

log₅x = 2

5² = x

x = 25

Example 5: Solve for z in the equation 5^2z-1 =1?

Solution:

5^2z-1 =1

2z-1=0

2z=1

z=1/2

Value of Log 5 - Practice Questions

Various practice questions on value of log 5 are,

Q1: Evaluate log5²

Q2: Determine the value of log√5

Q3: Find the exact value of log 125

Q4: Solve for x for the equation 10^x=5

Q5: Simplify log(5²×5³)

Q6: Determine the value of log√25

Q7: Simplify log 5^-2

Q8: Calculate the value of log(5×5)

Q9: If e^p=5, find the value of p

Q10: If e^x=25, find the value of x