The use of the nonuniform common (base 10) log scale permits detail for a wide range of values.
Use a semilog plane to display graphs with an exponential or a power or a large yrange and a small xrange where yvalues are all the same sign  negative or positive.
Use the loglog plane to display graphs were both xrange and yrange vary greatly.
Cubing Function, y = x^{3} 
Cubing Function, y = x^{3}, on semilog paper
Note that the extended lines on the yscale are for powers of 10: 1 or 10^{0}, 10 or 10^{1}, 100 or 10^{2}, 1000 or 10^{3}. 
Cubing Function, y = x^{3}, other domain values
Note that this graph can't be drawn using a log scale because all y values must have the same sign. 
The Exponential Function, y = e^{x}
The constant e is the base of the natural log, ln. 
The Exponential Function, y = e^{x}, on semilog plane
On a semilog plane, exponential growth is linear. 
Exponential & Power Functions, y = ab^{x} and y = ax^{m} on semilog plane
Use a graph on semilog or loglog planes to help determine if a function is exponential or power. On a semilog plane, exponential growth is linear. On a loglog plane, a power function is linear and the slope, m, through points (x_{1}, y_{1}) and (x_{2}, y_{2}) is
and very like the traditional coordinate plane slope formula. 
A Bland LogLog Plane w/Scales Marked
This is an example of how one might vary both scales and still keep accuracy. 
