# Exponential and Logarithmic Function TRENT M MAAS
Get Started. It's Free Exponential and Logarithmic Function ## 1. Section 1: Exponential Functions

### 1.1. Problems Involving Growth and Decay

1.1.1. Use these equations: A=P(e)^rt, A=P(1+(r/n)^nt, N=No(1+r)^t, N=No(e)^kt.

1.1.2. Solve using a graph or by hand.

1.1.3. When using a graph to solve graph both sides and find the intercept.

### 1.2. Basics of Exponential Functions

1.2.1. In y=ab^x, a can't be 0 and can't be 1

### 1.3. Transformations of Exponential Functions

1.3.1. HDRV

1.3.2. y=k+a(b)^(x-h)

### 1.4. Graphing Exponential Functions

1.4.1. Function has the form of f(x)=ab^x.

1.4.2. Important points include (-1,.5), (0,1), (1,2).

1.4.3. Has a horizontal asymptote at y=0.

## 2. Section 2: Logarithmic Functions

### 2.1. Logs are just exponents

2.1.1. log(2)4=2, 2^2=4

### 2.2. Evaluating Logs

2.2.1. Step 1: In log(3)81 set it equal to x.

2.2.2. Step 2: Put it into exponential form.

2.2.3. Step 3: Make all terms have the same base.

2.2.4. Step 4: Use prop. of equality for exponents then solve.

### 2.3. Properties of Logs

2.3.1. Common log has a base of ten and natural log has a base of e.

2.3.2. log(b)b^x=x, b^log(b)x=x

### 2.4. Graph of a log

2.4.1. Inverse of Exponential Functions

2.4.2. Asymptote at x=0

2.4.3. Important points at (.5,-1),(1,0),(2,1).

2.4.4. HDRV

## 3. Section 3: Properties of Logs

### 3.1. Properties of Logs

3.1.1. Product Property

3.1.2. Quotient Property

3.1.3. Power Property

## 4. Section 4: Expon. & Log. Equations

### 4.2. Solving Logarithmic Equations

4.2.1. Condense if possible then use One-to-One property. Check for Extraneous Solutions.

### 4.3. Solving Exponential equations

4.3.1. With problems with an uncommon base take the log of each side and solve.

4.3.2. Exponential Equations in Quadratic Form can be solved through factoring.

## 5. Section 5: Modeling with Non-Linear Regression

### 5.1. Exponential Regression

5.1.1. Step 1: Make a scatter plot.

5.1.2. Step2: Find an exponential function to model the data.

5.1.3. Step 3: Graph the scatter plot and equation on the same screen.

5.1.4. Step 4: Use the model to make a prediction.

5.1.5. Do these steps with a variety of different types of graphs and use the best fit.

5.1.6. The graph with the r^2 value closest to one is the best fit.