Let's go through the steps to calculate the negative log of 0.75. Just a note before we begin, we typically use the natural logarithm or the base 10 logarithm for such calculations. Since the context is pH, which uses base 10, we will proceed with base 10 logarithms.
a) Calculate the log of 0.75:
First, we take the base 10 logarithm of 0.75. To do this on a scientific calculator, you would simply enter 0.75 and hit the log button (which refers to base 10). The log of a number less than 1 is negative; for 0.75 it should be approximately -0.1249. This is because logarithms are exponents, and you are trying to find what power you must raise the base (which is 10 in this case) to get the number 0.75. Since 10 to the power of 0 is 1, and 10 to the power of -1 is 0.1, it makes sense that 10 raised to a power between 0 and -1 would give a number between 1 and 0.1, such as 0.75.
Note: The answer you obtain on the calculator may vary slightly due to rounding.
b) Take the negative of the answer:
The negative of the log value is simply the opposite sign of our result from the first step. If the log of 0.75 is -0.1249, then the negative log of 0.75 is the positive version of this number since two negatives make a positive.
Therefore, the -log(0.75) is approximately 0.1249.
So, in summary:
- The log of 0.75 (log(0.75)) is somewhere around -0.1249.
- The negative log of 0.75 (-log(0.75)) is then approximately 0.1249.
This concept of taking the negative logarithm is particularly used when calculating the pH of a solution in chemistry, where pH is defined as the negative base 10 logarithm of the concentration of hydrogen ions in a solution.
