Lesson 10

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. \(\log_2 35\)

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?

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 \(a^2  = b\).

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.

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.

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. \(\left(\frac12\right)^? = 2\)

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

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