Unless you’re a Math major or taking a math-related course, you may not be familiar with what logarithms are. Because of its formula, you might even say that they’re quite intimidating! However, logarithms aren’t that hard to understand.
To put it simply, logarithms are the opposite of exponents. Exponents are the quantity that represents the power to which a value X is raised.
Take the following example:
105 = 10 multiplied by itself 5 times
= 10 x 10 x 10 x 10 x 10
= 100,000
When expressed as a logarithmic function, it looks like this:
log10 (100,000) = 5
In this expression, you found out how many times 10 (in the log10) needs to be raised to have a value of 100,000. The answer is 5.
Now, if you want a formula that you can memorize, this is the relationship between exponents and logarithms:
ay = x is the logarithmic function that corresponds to loga (x) = y
Scientists and mathematicians value the power of logarithms because of how useful they are for solving exponential equations. One incredibly useful and life-saving example is the use of logarithms for the Richter Scale.
The Richter scale uses a logarithmic function to measure the magnitude of earthquakes in relation to other earthquakes. The value of R is the relationship between the magnitude of an earthquake and how much energy the quake released.
The value of the R essentially answers the question, “how much more intense is earthquake A than earthquake B when you compare them on the Richter scale?”
Logarithms are more common than you think. It answers the question “How many times do I have to multiply this number (a) by itself for me to get this other number (x)?”
For example, your math-loving parents tell you that they’ll give you some money. They’ll give you $2 (a) today, but they’ll multiply that amount by itself each time a day passes. However, their limit is $1,000. If you ask for the money before the value of the money reaches $1000, you’ll get it in full. If you ask for your money after it reaches a value of $1,000, you’ll get nothing. How many days should you wait before asking for your money to make sure you can get the maximum amount?
The question here is this:
Log$2 ($1000) = number of days you should wait before asking for your money
When you enter this into the Log Calculator, you must input a logarithm of $1000 with a base of $2. This gives you the value 9.965984. Since you can only count the days and not the fraction of a day, you must ask for your money on the 9th day.
On the 9th day, you’ll get exactly $512. This is the most money you can get that’s less than $1000 because, on the next day, the value would be $1024.
Using the Log Calculator is incredibly easy because you only need to input two of the following: the logarithm, the base, and what its logarithm is in relation to the base. Since most logarithmic equations give you two values, finding out the third is easy.
Take the mathematical expression below:
log5 (625) = x
In the Log Calculator, you have a logarithm of 625 and a base of 5. When you input these two things into the calculator, you’ll get the value of 4. This means that when you raise 5 to the power of 4 or 54, you get the value 625.
Try out the Log Calculator, one of the easiest ways to compute a logarithm!
