AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.10 Inverses of Exponential Functions
Notes
$f(x)=b^x$ and $g(x)=\log_bx$ are inverses.
- $b^{\log_bx}=x$ and $\log_b(b^x)=x$.
- Domain and range swap: $b^x$ has range $(0,\infty)$, so $\log_bx$ has domain $(0,\infty)$.
Practice
The inverse of $f(x)=5^x$:
Exponential and log with the same base.
$10^{\log_{10}7}=$
They undo each other.
The domain of $\log_3x$:
It's the range of $3^x$.
Ready for more? Take the Unit 2 test.