# Logarithmic practice problems

Practice logarithms below using the "rules" that you have just learned. Answers are provided (but try doing them on your own before peeking!)
**Problem 1. Suppose that you test pineapple juice and find that the hydrogen ion concentration is [H**^{+}] = 0.0003 M. Find the pH value and determine whether the juice is basic or acidic.

Solution.

Step 1: The exponent is the power of ten

0.0003 is the same as 3 x 10^{-4}

Step 2: Using the equation pH = -log_{10} of [0.0003] (in your calculator, hit log (0.0003), and then take the negative)

Answer: pH = 3.5 and this is acidic

**Problem 2. You test some ammonia and determine the hydrogen ion concentration to be [H**^{+}] = 1.3 x 10,sup>-9 M. Find the pH value and determine whether the ammonia is basic or acidic.

Solution.

Step 1: Since 1.3 is close to one, and 10-9 means it's close to pH 9, you could say that the approximate pH is a little lower than 9.

Step 2: Using the equation pH = -log_{10} of [1.3 x 10^{-9}] (in your calculator, hit log (1.3 x 10^{-9}), and then take the negative)

Answer: pH = 8.9 and this is alkaline

**Problem 3. Before fertilization, an egg cell has a calcium concentration of 1.2x10**^{-14}. When the sperm penetrates the cell membrane at the instant of fertilization, the calcium concentration increases to 2.4 x 10^{-5}. What is the magnitude of the increase in calcium in the cell?

Solution.

Step 1: Find the highest concentration of calcium and divide it by the lower concentration.

2.4 x 10^{-5}/ 1.2x10^{-14 }^{ }

2.4/1.2 x 10^{-5-(-14)} = 2 x 10^{9} about 2 billion times as much.