# Lesson 10

Interpreting and Writing Logarithmic Equations

- Let’s look at logarithms with different bases.

### Problem 1

- Use the base-2 log table (printed in the lesson) to approximate the value of each exponential expression.
- \(2^5\)
- \(2^{3.7}\)
- \(2^{4.25}\)

- Use the base-2 log table to find or approximate the value of each logarithm.
- \(\log_2 4\)
- \(\log_2 17\)
- \(\log_2 35\)

### Problem 2

Here is a logarithmic expression: \(\log_2 64\).

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

### Problem 3

- What is \(\log_{10}(100)\)? What about \(\log_{100}(10)\)?
- What is \(\log_{2}(4)\)? What about \(\log_{4}(2)\)?
- 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.

### 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.

### Problem 6

Find each missing exponent.

- \(10^?=100\)
- \(10^? = 0.01\)
- \(\left(\frac {1}{10}\right)^? = \frac{1}{1,000}\)
- \(2^? = \frac12\)
- \(\left(\frac12\right)^? = 2\)

### Problem 7

Explain why \(\log_{10}1 = 0\).

### Problem 8

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