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The logarithm of a number is another number which, if used as the exponent of a third number, yields the first number.

The third number is called the base. Usually, it is 10 (common logarithm) or e (2.71828..., natural logarithm).

As an example, the common logarithm of 100 is 2. This meets the equation...

102 = 100

... whereas the natural logarithm of 100 is about 4.61...

2.718284.61 = (about) 100

One useful function of logarithms is in the multiplication of numbers. If you want to multiply two numbers, you can either just multiply them, or you can add their logarithms together and do the inverse logarithm (power) of the result. For instance...

10 * 100 = 1000

log10 10 = 1

log10 100 = 2

1 + 2 = 3

103 = 1000

This technique is used in slide rules, and it can also be used visually, to come up with a rough estimate of the product of two numbers.

Q: Can you explain what the function of logarithms are?

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Natural logarithms use base e (approximately 2.71828), common logarithms use base 10.

you should include the definition of logarithms how to solve logarithmic equations how they are used in applications of math and everyday life how to graph logarithms explain how logarithms are the inverses of exponential how to graph exponentials importance of exponential functions(growth and decay ex.) pandemics, population)

The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.

explain why a function has at most one y-intercept

No, they are opposites, just like multiplication and division are opposites.

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Natural logarithms use base e (approximately 2.71828), common logarithms use base 10.

you should include the definition of logarithms how to solve logarithmic equations how they are used in applications of math and everyday life how to graph logarithms explain how logarithms are the inverses of exponential how to graph exponentials importance of exponential functions(growth and decay ex.) pandemics, population)

Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations .the present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century.

The base of common logarithms is ten.

The logarithmic function is not defined for zero or negative numbers. Logarithms are the inverse of the exponential function for a positive base. Any exponent of a positive base must be positive. So the range of any exponential function is the positive real line. Consequently the domain of the the inverse function - the logarithm - is the positive real line. That is, logarithms are not defined for zero or negative numbers. (Wait until you get to complex analysis, though!)

The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.The main misconception is that logarithms are hard to understand.

It turns out that many calculations and formulae are simpler if natural logarithms are used. To give but one example, the derivative (or slope) of the nagural logarithm function is 1/x. This means the derivative of other logarithms is more complicated.

explain why a function has at most one y-intercept

Logarithms were invented by John Napier who was a mathematician. He invented other things too, so there was no reason why he couldn't invent the logarithms. Logarithms were invented so people could take short cuts to multiplications! :)

In 1614, John Napier published his invention of logarithms.

No, they are opposites, just like multiplication and division are opposites.

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