Chapter 17 – Logarithms to Base 10 (L Scale)
Recall the Laws of Logarithms:
And the equivalent Logarithmic and Exponential form:
and
17.1 Logarithms and Antilogarithms Using L and D scales.
(i.e. usual L scale on body of the slide rule)
Fig 17-1
Example 1: (Fig. 17-1)
(Or this could be stated )
Note:
e.g. or
The Slide Rule gives us only the mantissa, as do logarithm tables.
Example 2: antilogarithm of 3.26 = 1,820
(or this could be stated )
(as the characteristic is 3)
(See exercise 17(a) at the end of 17.2 for problems)
Note:
As sines, cosines and tangents are found on the D scale, the value of log sin, log cos and log tan can be obtained by reading from the angle on the appropriate trigonometrical scale directly onto the L scale.
17.2 Logarithms and Antilogarithms Using L and W (Root) scales.
This is the system applicable to the Faber-Castell Slide Rules 2/83N, 62/83 etc. The L scale is on the slide and it is used in conjunction with the W scales. It is best to use the W’1 and W’2 scales instead of the W1 and W2 scales to avoid any error, should the slide be slightly displaced.
Example 1:
Example 2:
answer = 1.916 (as 82.4 is between 10 and 100).
Exercise 17(a)
Find X in the Following:
17.3 Raising Numbers to Powers and Solving Exponential Equations:
A. Raising a Number to Power. (A better method using LL scales is given in unit 19.)
Example 1:
Express as (by Law III)
(Using Slide Rule to Find logarithm)
(Multiply using Slide Rule)
(Use the Slide Rule again to obtain the antilog of 0.55 and position the decimal point according to the characteristic, 7.)
answer = 35,450,000
B. Solving an Exponential Equation.
Example 2: solve 3x = 5 for x
If two quantities are equal, then their logarithms will be equal.
i.e.
(evaluate each using Slide Rule)
(divide using Slide Rule)
(evaluate each using Slide Rule)
Exercise 17(b)
Find x in the following:
(Hint, write as )