The Inverse Relationship
An **exponential function** is a function where the variable is in the exponent, like $f(x) = b^x$. It represents rapid growth or decay.
A **logarithmic function** is the inverse of an exponential function. It answers the question: "What exponent do I need to raise the base to, in order to get this number?" The general form is $y = \log_b(x)$, which is equivalent to $b^y = x$.
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Video: Graphing & Properties!
Watch this video to visualize the inverse relationship between these two functions on a graph! 🔄
Practice Problems
Convert between exponential and logarithmic forms!
1) Write $4^3 = 64$ in logarithmic form.
2) Write $\log_2(8) = 3$ in exponential form.
3) What is $\log_{10}(1000)$?
4) What is the value of $x$ in $5^x = 25$?
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