But as
10
{\displaystyle 10}
100
{\displaystyle 100}
1000
{\displaystyle 1000}
2
{\displaystyle 2}
3
{\displaystyle 3}
0.4343
{\displaystyle 0.4343}
log
10
x
=
0.4343
×
log
ϵ
x
{\displaystyle \log _{10}x=0.4343\times \log _{\epsilon }x}
and conversely,
log
ϵ
x
=
2.3026
×
log
10
x
{\displaystyle \log _{\epsilon }x=2.3026\times \log _{10}x}
A Useful Tables of “Napierian Logarithms”
N
u
m
b
e
r
{\displaystyle Number}
log
ϵ
{\displaystyle \log _{\epsilon }}
N
u
m
b
e
r
{\displaystyle Number}
log
ϵ
{\displaystyle \log _{\epsilon }}
1
{\displaystyle 1}
0.0000
{\displaystyle 0.0000}
6
{\displaystyle 6}
1.7918
{\displaystyle 1.7918}
1.1
{\displaystyle 1.1}
0.0953
{\displaystyle 0.0953}
7
{\displaystyle 7}
1.9459
{\displaystyle 1.9459}
1.2
{\displaystyle 1.2}
0.1823
{\displaystyle 0.1823}
8
{\displaystyle 8}
2.0794
{\displaystyle 2.0794}
1.5
{\displaystyle 1.5}
0.4055
{\displaystyle 0.4055}
9
{\displaystyle 9}
2.1972
{\displaystyle 2.1972}
1.7
{\displaystyle 1.7}
0.5306
{\displaystyle 0.5306}
10
{\displaystyle 10}
2.3026
{\displaystyle 2.3026}
2.0
{\displaystyle 2.0}
0.6931
{\displaystyle 0.6931}
20
{\displaystyle 20}
2.9957
{\displaystyle 2.9957}
2.2
{\displaystyle 2.2}
0.7885
{\displaystyle 0.7885}
50
{\displaystyle 50}
3.9120
{\displaystyle 3.9120}
2.5
{\displaystyle 2.5}
0.9163
{\displaystyle 0.9163}
100
{\displaystyle 100}
4.6052
{\displaystyle 4.6052}
2.7
{\displaystyle 2.7}
0.9933
{\displaystyle 0.9933}
200
{\displaystyle 200}
5.2983
{\displaystyle 5.2983}
2.8
{\displaystyle 2.8}
1.0296
{\displaystyle 1.0296}
500
{\displaystyle 500}
6.2146
{\displaystyle 6.2146}
3.0
{\displaystyle 3.0}
1.0986
{\displaystyle 1.0986}
1
,
000
{\displaystyle 1,000}
6.9078
{\displaystyle 6.9078}
3.5
{\displaystyle 3.5}
1.2528
{\displaystyle 1.2528}
2
,
000
{\displaystyle 2,000}
7.6010
{\displaystyle 7.6010}
4.0
{\displaystyle 4.0}
1.3863
{\displaystyle 1.3863}
5
,
000
{\displaystyle 5,000}
8.5172
{\displaystyle 8.5172}
4.5
{\displaystyle 4.5}
1.5041
{\displaystyle 1.5041}
10
,
000
{\displaystyle 10,000}
9.2104
{\displaystyle 9.2104}
5.0
{\displaystyle 5.0}
1.6094
{\displaystyle 1.6094}
20
,
000
{\displaystyle 20,000}
9.9035
{\displaystyle 9.9035}
Exponential and Logarithmic Equations .
Now let us try our hands at differentiating certain expressions that contain logarithms or exponentials.
Take the equation:
y
=
log
ϵ
x
{\displaystyle y=\log _{\epsilon }x}
First transform this into
ϵ
y
=
x
{\displaystyle \epsilon ^{y}=x}
