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It is because exponential functions are one-to-one. Whether you want to use logarithms or not they exist because a bijective function has an inverse. Logarithms put numbers on a human-friendly scale, such as the Richter scale, the Decibel scale, etc...
2. Why do we study logarithms ? In order to motivate our study of logarithms, consider the following: we know that 16 = 24. We also know that 8 = 23 Suppose that we wanted to multiply 16 by 8. One way is to carry out the multiplication directly using long-multiplication and obtain 128.
In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. We write it like this: So these two things are the same:
Logarithms are a convenient way to express large numbers. (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division.
27 Αυγ 2020 · A logarithm is the answer to the question what power x do I need to apply to the base b in order to obtain the number y: log_b(y) = x is another way of specifying the relationship: b^x = y. Let’s plug in some numbers to make this more clear. We will do base-10, so b=10. log_10(100) = 2 The base-10 logarithm of 100 is 2 because: 10^2 = 100
Logarithms make a lot of people anxious. A lot of this has to do with the way they're often taught in high school and secondary school: by memorizing all the proper steps, without imparting much deeper meaning. For example, maybe you were once taught to solve problems like this: log7 49 = ?
traditional study of logarithms, we have deprived our students of the evolution of ideas and concepts that leads to deeper understanding of many concepts associated with logarithms. As a result, teachers now could hear “(5.2)y = 30.47, y = 6.32 because the calculator says so,” (52 = 25 for goodness sakes!!)
