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C25 - solving problems involving exponential and logarithmic equations

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**Lindsay**

## Definitions:

**Exponential Equation:** an equation involving an exponential function of a variable

**Example:**

**What this is saying:** 3 to the power of x is equal to 27.

**Logarithmic Equation:** an equation involving a log function of a variable

**Example:**

**What this is saying:** 3 to the power of x is equal to 27.

They say the same thing?!

Yes!! They say the same thing because they are the same thing!

# =

**How to convert from an exponential equation to a logarithmic eqaution:**

First, let's indentify the parts of an each equation:

The **3** is the **BASE**. The **x** is the **EXPONENT**. The **27** is the **SOLUTION**.

To make this a logarithm, you have to change some things around.

The **BASE** of a logarithmic equation is the same **BASE** from the exponential equation, but the **EXPONENT** and **SOLUTION** change places.

The **3** is still the **BASE**. The **27** is now called the **ARGUEMENT**. The **x** is the **SOLUTION**.

**To solve a logarithmic equation: **Since a calculator will only do logarithms of **log base 10**, you need to use the **CHANGE OF BASE** formula. This is taking the **log base 10** of the **ARGUEMENT** divided by the **log base 10** of the **BASE**. The answer you'll get will equal **x**.

Example:

**Now try some on your own!!** I'll give examples of changing from an exponential equation to a logaritmic equation and back. **Solve for x in each question.**

**Answers:**

a) x=4 b) x=2 c) x=6 d) x=4096 e) x=216

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## Comments (1)

## Anonymous said

at 9:19 pm on Apr 29, 2007

Nice job Lindsay. This is an advanced class however, how about a little more challenging sample question with a worked out solution instead of just the answer.

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