Plane trigonometry, by S.L. Loney.

LOGARITHMS TO BASE 10. 303
We can convert these logarithms into logarithms to
base 10.
For, by Art. 147, we have, if N be any number,
log, V = log0, N x log, 10.. log, N=loge N x
log, 10'
Now log, 10 can be found as in the last article and
then I 1is found to be -4342944819...
log, 10
Hence logo N = log, N x -43429448...,
so that the logarithm of any number to base 10 is found
by multiplying its logarithm to base e by the quantity
~43429448.... This quantity is called the Modulus.
EXAMPLES. XLVI.
Prove that
1. 1(e+e)=l+..
2. (1+Il 31- I 12 13.. )-1.
( 1 1 21 )1 2
3. ++
2 3 4 e 2 4 6. 1+3 ++....t = 5. + + +....~-"'.
12112 14
I 1 1
+ --- T_++
6, - _ ____ e-l
1 1 =e- '
1++ +...
23 33 43
7. 1 + + F + F + =5e.
7. 2 1++~~...