5.5 Solving Exponential Equations and Logarithmic Equations

  • Solve exponential equations.

  • Solve logarithmic equations.

Solving Exponential Equations

Equations with variables in the exponents, such as

3x=20  and  25x=64,

are called exponential equations.

Sometimes, as is the case with the equation 25x=64, we can write each side as a power of the same number:


We can then set the exponents equal and solve:

5x=6x=65,  or  1.2.

We use the following property to solve exponential equations.

This property follows from the fact that for any a>0, a1, f(x)=ax is a one-to-one function. If ax=ay, then f(x)=f(y). Then since f is one-to-one, it follows that x=y. Conversely, if x=y, it follows ...

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