# 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