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