What Are Exponential Equations?
An exponential equation has the variable in the exponent, like \( 2^x = 32 \).
Method 1: Same Base
If you can express both sides with the same base, set exponents equal.
Example: \( 2^x = 32 \). Since \( 32 = 2^5 \), we get \( x = 5 \).
Method 2: Using Logarithms
When same base is not possible, take the log of both sides.
Example: \( 3^x = 20 \)
\( x = \frac{\log 20}{\log 3} \approx 2.727 \)
Properties of Exponents
- \( a^m \cdot a^n = a^{m+n} \)
- \( (a^m)^n = a^{mn} \)
- \( a^0 = 1 \)
Try exponential equations on our Algebra 2 Solver!
