# Lesson 10

Interpreting and Writing Logarithmic Equations

• Let’s look at logarithms with different bases.

### Problem 1

1. Use the base-2 log table (printed in the lesson) to approximate the value of each exponential expression.
1. $$2^5$$
2. $$2^{3.7}$$
3. $$2^{4.25}$$
2. Use the base-2 log table to find or approximate the value of each logarithm.
1. $$\log_2 4$$
2. $$\log_2 17$$
3. $$\log_2 35$$

### Problem 2

Here is a logarithmic expression: $$\log_2 64$$.

1. How do we say the expression in words?
2. Explain in your own words what the expression means.
3. What is the value of this expression?

### Problem 3

1. What is $$\log_{10}(100)$$? What about $$\log_{100}(10)$$?
2. What is $$\log_{2}(4)$$? What about $$\log_{4}(2)$$?
3. Express $$b$$ as a power of $$a$$ if $$a^2 = b$$.

### Problem 4

In order for an investment, which is increasing in value exponentially, to increase by a factor of 5 in 20 years, about what percent does it need to grow each year? Explain how you know.

(From Unit 4, Lesson 4.)

### Problem 5

Here is the graph of the amount of a chemical remaining after it was first measured. The chemical decays exponentially.

What is the approximate half-life of the chemical? Explain how you know.

(From Unit 4, Lesson 7.)

### Problem 6

Find each missing exponent.

1. $$10^?=100$$
2. $$10^? = 0.01$$
3. $$\left(\frac {1}{10}\right)^? = \frac{1}{1,000}$$
4. $$2^? = \frac12$$
5. $$\left(\frac12\right)^? = 2$$
(From Unit 4, Lesson 8.)

### Problem 7

Explain why $$\log_{10}1 = 0$$.

(From Unit 4, Lesson 9.)

### Problem 8

How are the two equations $$10^2 = 100$$ and $$\log_{10}(100) = 2$$ related?

(From Unit 4, Lesson 9.)