Semi-log Plots

about 30 min · 6 short parts · stop after any part

Is this data exponential? A semi-log plot answers it at a glance: exponential data turns into a straight line.
By the end you can read one, spot fakes, and turn

y=ab^x

into a line.

The path

1
Log tools you need
You can split $\log(5\cdot 2^x)$ and undo $\log y = 2.3$ .
2
Reading a semi-log plot
You can place a value like 300 on a log-scaled $y$ -axis.
3
Why exponential turns straight
You can turn $y = ab^x$ into the line $\log y = \log a + x\log b$ .
4
Exponential or not? Check the axes
You can say if a graph shows exponential data, and why.
5
Linearize real data
You can get $y = ab^x$ and its line $\log y = mx + B$ from a table.
6
Mixed review in the homework
You can combine logs, combine powers, and solve with a domain check.