WOLFRAM|DEMONSTRATIONS PROJECT

A Visualization of Logarithms

​
a
3
b
0.8
Let
R
,
B
,
O
,
G
stand for the areas of the regions colored red, blue, orange, and green, respectively.
In the right graphic, observe that
R=B+O
. Moreover,
O=G
, because:
O=
1
a
a
a
2
-
1
a
b
a
2
=
a-b
2a
and
G=
b
a
+
b
b
2
1
b
-
1
a
=
a-b
2a
.
Therefore the red area is
R=B+O=B+G=
1
2
ln
a
b
.
In the case
b=
1
a
,a>1
, the red area is
lna
.