Plane trigonometry, by S.L. Loney.

156

TRIGONOMETRY.

In the table of logarithms we find, opposite the number 12340 the
logarithm 0913152, so that
log -12340 = 10913152.
Hence log x= log 12340 nearly,
and therefore x= 12340 nearly.
When the logarithm of any number does not quite agree with any
logarithm in the tables but lies between two consecutive logarithms, it
will be shewn in the next chapter how the number may be accurately
found.
Ex. 8. Iaving given log2=-30103, find the nuimber of digits in 267
and the position of the first significant figure in 2-37.
We have log 2 = 67 x log 2 = 67 x -30103
=20-16901.
Since the characteristic of the logarithm of 267 is 20 it follows, by Art.
142, that in 267 there are 21 digits.
Again log 2-37= - 37 log 2 = - 37 x -30103
= -1113811= 12-86189.
Hence by Art. 142, in 2-37 there are 11 cyphers following the decimal
point, i.e. the first significant figure is in the twelfth place of decimals.
Ex. 4. Given log3=4771213, log7= - 8450980and log11=1-0413927,
solve the equation
3x x 72x+l= 11+5
Taking logarithms of both sides we have
log 3x + log 72"+1 = log 11x+5..x. log 3 +(2 + 1)log7=(x + 5)log 11..-. x[log 3 + 2 log 7 - log] = 5 log 11 - log7.
5 log 11 - log 7
" log 3+ 2 log 7 - log 11
5_2069635 - -8450980
- 4771213 + 1-6901960 - 10413927
4-3618655
= -11259246 7 387.
1~1259246 -