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:
loge5 = 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:
logba = logca / logca
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
- Identify the Characteristics: Locate the logarithmic table and identify the columns for the integer part and decimal part of the logarithm.
- Find the Integer Part: In the table, find the entry corresponding to the whole number part of log5, which is 0 in this case.
- Find the Decimal Part: Locate the row that corresponds to the first two digits after the decimal point. For log5, it would be 69.
- 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.
- 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
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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 10x = 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 5y=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 52z-1 =1?
Solution:
52z-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 10x=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 ep=5, find the value of p
Q10: If ex=25, find the value of x
Value of Log 5 - FAQs
What is Value of log 5?
Value of log5 is approximately 0.69897.
How can I interpret the value of log 5?
log5 represents the exponent to which 10 must be raised to yield the value 5. It is a logarithmic expression commonly used in mathematical calculations.
What is Value of log 5 base 5?
Value of log 5 base 5 is 1
What is the Relationship between log5 and log 1/5?
log 1/5 is the negative of log5. In other words, log 1/5= −log5.
If ax =5, what is the value of x?
To find x, you can use= loga5. If the base is not specified, it is assumed to be 10.
Can log5 be simplified further?
log5 is already in its simplest form. It is a decimal approximation and not expressed as a fraction.
How do I solve log 5 problems in different bases?
If the base is different from 10, you can use the change of base formula, such as loga5= logb5/logba.
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