Quick Answer: How Do You Explain Logarithms?

How was logarithms invented?

The Scottish mathematician John Napier published his discovery of logarithms in 1614.

His purpose was to assist in the multiplication of quantities that were then called sines.

The whole sine was the value of the side of a right-angled triangle with a large hypotenuse..

What is log10 equal to?

The value of log1010 is equal to 1. The value of loge10 which can also be written as ln (10) is 2.302585.

What is the difference between a logarithm and an algorithm?

What is the difference between Algorithm and Logarithm ? Answer : Algorithm is a noun meaning some special process of solving a certain type of problem. … Whereas logarithm, again a noun, is the exponent of that power of a fixed number, called the base, which equals a given number, called the antilogarithm.

How do engineers use logarithms?

All types of engineers use natural and common logarithms. Chemical engineers use them to measure radioactive decay, and pH solutions, which are measured on a logarithmic scale. Exponential equations and logarithms are used to measure earthquakes and to predict how fast your bank account might grow.

How do you sum a log?

Logs of the same base can be added together by multiplying their arguments: log(xy) = log(x) + log(y). They can be subtracted by dividing the arguments: log(x/y) = log(x) – log(y).

What is another name for logarithm?

What is another word for logarithm?numericarithmeticintegratedlogarithmicmathematicalnumeralnumerarynumericalstatistical4 more rows

What are the 3 laws of logarithms?

Rules of LogarithmsRule 1: Product Rule. … Rule 2: Quotient Rule. … Rule 3: Power Rule. … Rule 4: Zero Rule. … Rule 5: Identity Rule. … Rule 6: Log of Exponent Rule (Logarithm of a Base to a Power Rule) … Rule 7: Exponent of Log Rule (A Base to a Logarithmic Power Rule)

What are different kinds of logarithms used?

Having learned about logarithms, we can note that the base of a logarithmic function can be any number except 1 and zero. However, the other two special types of logarithms are frequently used in mathematics. These are common logarithm and natural logarithm.

Are logarithms hard?

No. I’ve never understood why people think logarithms are hard; it’s very common for people to feel uncomfortable with them. Trigonometric functions are harder to deal with but people tend to be more comfortable with them than logarithms.

How does a logarithm work?

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. The logarithm of a product is the sum of the logarithms of the factors. The logarithm of the ratio or quotient of two numbers is the difference of the logarithms.

How do we use logarithms in real life?

Exponential and logarithmic functions are no exception! Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

What are the log rules?

The rules apply for any logarithm logbx, except that you have to replace any occurence of e with the new base b. The natural log was defined by equations (1) and (2)….Basic rules for logarithms.Rule or special caseFormulaQuotientln(x/y)=ln(x)−ln(y)Log of powerln(xy)=yln(x)Log of eln(e)=1Log of oneln(1)=02 more rows

What is a log of 1?

log 1 = 0 means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. Therefore, ln 1 = 0 also.

Can the base of a log be negative?

While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. … To understand why, we have to understand that logarithms are actually like exponents: the base of a logarithm is also the base of a power function.

Does log have a limit?

Just like exponential functions, logarithmic functions have their own limits. Remember what exponential functions can’t do: they can’t output a negative number for f (x). The function we took a gander at when thinking about exponential functions was f (x) = 4x.

What is a logarithm in simple terms?

A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

What is the purpose of logarithms?

It lets you work backwards through a calculation. It lets you undo exponential effects. Beyond just being an inverse operation, logarithms have a few specific properties that are quite useful in their own right: Logarithms are a convenient way to express large numbers.