Solving Exponential Equations
Key points
- When solving exponential equations:
- Use the same base if you are using laws of exponents.
- Usually when there are exponential expressions on either side of the equation
- Use logarithms to solve for unknown exponents.
- Use the same base if you are using laws of exponents.
When there are exponential expressions on either side of the equation, as seen in the example to the right, use laws of exponents to simplify as much as possible.
- Converting to the same base is the first step in the solving strategy.
- Needed whenever using laws of exponents.
- Simplify as much as possible using laws of exponents.
- Cancel the common bases, and set exponents equal each other, then solve for x.
When exponential expressions are equal to a value use logarithms to solve.
- This value will be either given, or found by simplifying another exponential expression on the other side of the equation.
- Convert the exponential equation to a logarithmic equation to solve for the unknown values.
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