find log of 7.653 ?
Answers
Explanation:
x log(x) 1 0 1.001 0.00043408 1.002 0.00086772 1.003 0.00130093 1.004 ... 7.651 0.8837182 7.652 0.88377496 7.653 0.88383171 7.654 0.88388846 7.655 0.8839452
Answer:
Log 1 0
Log 2 0.3010
Log 3 0.4771
Log 4 0.6020
Log 5 0.6989
Log 6 0.7781
Log 7 0.8450
Log 8 0.9030
Log 9 0.9542
Log 10 1
Natural Logarithm Table For 1 To 10
Here we have provided natural logarithmic values table for 1 to 10:
Natural Logarithm to a Number (logex) Log Values
ln (1) 0
ln (2) 0.693147
ln (3) 1.098612
ln (4) 1.386294
ln (5) 1.609438
ln (6) 1.791759
ln (7) 1.94591
ln (8) 2.079442
ln (9) 2.197225
ln (10) 2.302585
Get Algebra formulas for Class 8 to 11 below:
Algebra Formulas for Class 8 Algebra Formulas for Class 9
Algebra Formulas for Class 10 Algebra Formulas for Class 11
Solved Examples On Logarithm Formula Table
Here we have provided some of the sample questions and answers on log table 1 to 100:
Question 1: Find the value of log10 8.675
Solution: The value can be obtained in the following steps:
Step 1: Integer = 8 and Decimal = 675
Step 2: Check the row number 86 (first two digits of the given number) and column number 7 (third digit of the given number). So, the value obtained is 9380.
Step 3: Check the mean difference value for row number 86 and mean difference column 5. The value corresponding to the row and column is 3.
Step 4: Add the values obtained in step 2 and 3, we get 9383. This is the mantissa part.
Step 5: Since the number of digits to the left side of the decimal part is 1. So the characteristic part = (Number of digits to the left of the decimal – 1)
= 0
Step 6: Combine the characteristic and the mantissa part. So, it becomes 0.9383.
Therefore, the value of log10 8.675 is 0.9383.
Question 2: Find the value of log (45.67) using the log table.
Solution: 45.67 = 4.567 × 101
So, log (45.67) = log (4.567 x 10)
= log (4.567) + log (10) [Using the logarithm property: log (a.b) = log a + log b]
= log (4.567) + 1 [∵ log (10) = 1, for common log]
Now, let’s find the value of log (4.567).
Look up at a standard log table. Go to the row number 45 (first two digits of n) and column number 6 (third digit of n).
Note down the corresponding value which is 0.6590.
Now again go to the row number 45 and column number 7 (fourth digit of n) in the mean difference table.
Note down the corresponding value which is 7.
Now add the two values. We get: 0.6590 + 7 = 0.6597
This is the mantissa part.
Since, we are using a common log table, characteristic = (Number of digits to the left of decimal – 1)
= (1 – 1) = 0
∴ Characteristic = 0
Now, combine both the parts, we get log (4.567) = 0.6597
log (45.67) = log (4.567) + 1
= 0.6597 + 1
1.6597
Therefore, the value of log (45.67) is 1.6597
Question 3: Use log table to evaluate the following logarithmic function:
Solution: We can solve the value of N in 4 steps:
Step 1: Convert the expression for N into simple logs.
Step 2: Evaluate those logs using a log table.
Step 3: Determine the value of log N.
Step 4: Calculate the value of N using the antilog of log N.
So, logN = log(647⋅32×0.00000147 / 8.473×64)
= log(647⋅32) + log(0.00000147) − log(8.473) − log(64) [Using the product rule for logarithms]
Using the log table, we find the following values:
647.32 = 6.4732 × 102
⇒ log(647.32 )
= 2 + log(6.4732)
= 2 + 0.8111
= 2.8111
0.00000147 = 1.47×10-6
⇒ log(0.00000147) = −6 + log(1.47)
= -6 + 0.1673
8.473 = 8.473×100
⇒ log(8.473) = 0.9280
64 = 6.4 × 101
⇒ log(64) = 1 + log(6.4)
= 1.8062
∴ logN = 2.8111 + (-6 + 0.1673) – 0.9280 – 1.8062
= –5.7558
= –5 – 0.7558
= (–5 – 1) + 1 – 0.7558 [∵ mantissa cannot be negative, we have added and subtarcted 1 to make it positive]
= –6 + 0.2442
Now, we have the characteristic = -6 and the mantissa = 0.2442.
To find the value of N, we use the formula:
N = antilog (Mantissa) × 10Characteristic
= antilog (0.2442) x 10-6
= 1.7547 x 10-6 [Using the antilog table]
⇒ N = 1.7547 × 10-6
= 0.0000017547
Hence, the value of N is 0.0000017547. You can verify the value using a calculator.
Practice Questions On Standard Logarithm Table
Here we have provided some of the practice questions on the mathematical log table for you to practice:
Q1: Find logarithm values of the following to the base 10 using log table:
(i) 7.653
(ii) 14.25
(iii) 9.281
Q2: If 3 + log10 x = 2 log10 y, find x in terms of y.
Q3: Prove that, 7 log (10/9) + 3 log (81/80) = 2log (25/24) + log 2.
Q4: If log10 2 = 0.30103, log10 3 = 0.47712 and log10 7 = 0.84510, find the values of:
(i) log10 45
(ii) log10 105
Q5: If log 9 = b and log 5 = c, evaluate log 75 in terms of b and c.
Frequently Asked Questions On Log Table Math
Here we have provided some of the FAQs related to online log tables that we have provided in this article.
Q1: How do you read a log table?
A: Take the first 2 digits of the number irrespective of the decimal and look for the row with that number. Next look for the column number corresponding to the third digit of the number. You may also need to look into the mean difference table to get the final value. The step-by-step process to read a log table is provided on this page.
Q2: What is the value of log 1