LOGARITHMS AND TRIGONOMETRICAL RATIOS 85

so that 2588 x-9848=8in 15° x Cos 10°, and this gives the
following values to be substituted in (iv) above:

A=15°
B=10°
A+B=25°
A—B= 5°

and we obtain:
Sin 15°.Cos 10°=%(Sin 25°+-Sin 5°)
From the tables of sines, we find:
Sin 25°=-4226
Sin  5°=-0872
so that
3(Sin 25°+Sin 5°) =1(-4226 +-0872) =-2549
therefore
2588 X 9848 =-2549
To multiply these same two numbers by the use of loga-
rithms, we have:
Log 2588 =1-4130
Log 9848 =1-9934

Add: 1-4064

 

 

Antilog 1-4064 =-2549

Logarithms calculated to one base number may very
easily be converted to another base. The logarithm of the
number 4 to the base of 2 is obviously 2, since 4=22. On the
other hand, the logarithm of the number 4 to the base of
10 is ‘6021.

Thus: Log, 4=20

Log;, 4= -6021

If we divide the first logarithm (to the base of 2) by the
second logarithm (to the base of 10), we obtain the ratio
3-322, and this ratio proves to be the logarithm of the second
base number when calculated to the first base. That is:

Log, 10=3-322

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