Exponential and Logarithmic Equations
Learning Objectives:
1. Solve logarithmic equations using the
properties of logarithms.
2. Solve exponential equations.
3. Solve equations involving exponential
models.
1. One-to-One Property of Logarithms
One-to-One Property of Logarithms
In the following property, M, N, and a are positive real
numbers, with a ≠ 1.
If logaM = logaN, then M = N.
Example:
![](./articles_imgs/6234/expone36.jpg)
Check:
1. Solving Logarithm Equations
Example: Solve:
![](./articles_imgs/6234/expone2.gif) ![](./articles_imgs/6234/expone3.jpg)
Example: Solve:
![](./articles_imgs/6234/expone4.gif) ![](./articles_imgs/6234/expone5.jpg)
2. Solving Exponential Equations
Example:
![](./articles_imgs/6234/expone6.jpg)
Example:
Solve:
![](./articles_imgs/6234/expone7.gif)
3. Exponential Models
The compound interest formula states that the future value of P
dollars invested in an account paying an annual interest rate r,
compounded n times per year for t years, is given by
![](./articles_imgs/6234/expone37.jpg)
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