AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.15 Semi-log Plots
Notes
A semi-log plot uses a log scale on the $y$-axis. Exponential data appear as a straight line.
- If $y=ab^x$, then $\log y=\log a+x\log b$: linear in $x$.
Practice
Data on a semi-log plot form a straight line. The original data are:
Logging exponential data makes it linear.
For $y=ab^x$, the slope of the line on a semi-log plot ($\log y$ vs $x$) is:
$\log y=\log a+(\log b)x$.
The $\log y$-intercept on that plot equals:
At $x=0$, $\log y=\log a$.
Ready for more? Take the Unit 2 test.