# Question bank: Logarithms: Introduction

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Question 1:

Medium

You are assisting a friend in organizing his book collection and he wants to categorize them in a way that he can easily find any book on a shelf with 1000 shelves. He decides to use a base 10 logarithm system to label the shelves, where each number from 1 to 1000 will be transformed into its corresponding logarithm. What would be the label of the shelf corresponding to book number 500, applying the properties of logarithms to simplify the expression?
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Question 2:

Medium

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Question 3:

Medium

In a Chemistry class, you learned about calculating the pH of acidic and alkaline solutions and the relationship between pH and the concentration of hydrogen ions [H+]. The pH can be calculated using the formula pH = -log([H+]), where [H+] represents the concentration of hydrogen ions in mol/L. If you found that the concentration of hydrogen ions in a solution is 1 x 10⁻⁵ mol/L, what is the approximate value of the pH of this solution?
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Question 4:

Medium

In a bacterial population growth experiment, a biologist noticed that the population of bacteria doubled every 3 hours. He decided to model this growth using an exponential function with base 2. If the biologist started the experiment with a single bacterium, how many hours would it take for the population to reach 1 million bacteria? Use logarithms to solve the problem.
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Question 5:

Medium

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