- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Q.1 Find the common logarithm of each of the following numbers.
(i) 232.92
(iii) 0.00032
(ii) 29.326
(iv) 0.3206
Solution:
To find the common logarithm of a number, we take the logarithm of the number with base 10. The common logarithm is often denoted as “log” without a subscript, which implies base 10. Here’s how to find the common logarithm of each of the given numbers:
(i) 232.92:
log(232.92) ≈ 2.36621
(ii) 29.326:
log(29.326) ≈ 1.46626
(iii) 0.00032:
log(0.00032) ≈ -3.49485
(iv) 0.3206:
log(0.3206) ≈ -0.49399
Please note that the logarithms are approximate values rounded to five decimal places. You can use a calculator with logarithmic functions to find more precise values if needed.
Q.2 If log 31.09=1.4926, find values of the following
(i) log(3.109) (ii) log(310.9) (iii) log 0.003109 (iv) log 0.3109
Solution:
Given that log 31.09 = 1.4926, we can use this information to find the values of the following logarithms:
(i) log(3.109):
To find log(3.109), we need to identify the relationship between 3.109 and 31.09. Notice that 31.09 is exactly 10 times larger than 3.109 (31.09 = 10 * 3.109). Since logarithms measure the power to which the base (10) must be raised to get the number, we can use this relationship to find log(3.109):
log(3.109) = log(31.09) – log(10)
log(3.109) = 1.4926 – 1 (since log(10) = 1)
log(3.109) = 0.4926
(ii) log(310.9):
Similarly, to find log(310.9), we recognize that 310.9 is exactly 100 times larger than 3.109 (310.9 = 100 * 3.109). So we can use this relationship to find log(310.9):
log(310.9) = log(31.09) + log(10)
log(310.9) = 1.4926 + 1 (since log(10) = 1)
log(310.9) = 2.4926
(iii) log 0.003109:
To find log 0.003109, we can rewrite the number as 3.109 * 0.001:
log(0.003109) = log(3.109 * 0.001)
log(0.003109) = log(3.109) + log(0.001)
log(0.003109) = 1.4926 – 3 (since log(0.001) = -3)
log(0.003109) = -1.5074
(iv) log 0.3109:
To find log 0.3109, we can rewrite the number as 3.109 * 0.1:
log(0.3109) = log(3.109 * 0.1)
log(0.3109) = log(3.109) + log(0.1)
log(0.3109) = 1.4926 – 1 (since log(0.1) = -1)
log(0.3109) = 0.4926