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in this lesson were going to focus on evaluating logs so what is log base 2 of 16 what is that equal to 2 raised to the what power is 16. how many twos do you have to multiply to get to 16 2 times 2 times 2 times 2 4 times 16 so therefore 2 to the fourth is 16. so log base 2 of 16 is equal to four so now that you know that what is log base 3 of 27 how many threes do you need to multiply to get to 27 you need to multiply 3 3 times it gets 27 3 times 3 times 3 is 27 so log base 3 of 27 is 3. now what about log base 5 of 25 how many fives do you have to multiply to get to 25 you need to multiply two fives five squared is 25. now what about log base four of one log of one is always equal to zero what about log base seven of seven to the first power is seven so if these numbers are the same they will cancel its simply one now what is log of a thousand what should you do if youre not given a base if there is no base its always assumed to be a ten so how many tens do you have to multiply

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Logarithms are used for measuring the magnitude of earthquakes. Logarithms are used for measuring the noise levels in dBs (decibels). They are used to measure the pH level of chemicals. Logarithms are used in radioactivity, mainly to detect the half life of a radioactive element.

log: (in math) An abbreviation for logarithm. logarithm: The power (or exponent) to which one base number must be raised multiplied by itself to produce another number. For instance, in the base 10 system, 10 must be multiplied by 10 to produce 100. So the logarithm of 100, in a base 10 system, is 2.

Logarithm Base Properties Product rule: am. an=a. m+n Quotient rule: am/an = a. m-n Power of a Power: (am)n = a. mn

Hence, the logarithm of 0.001 to the base 10 is equal to -3.

A logarithmic function will have the domain as (0, infinity). The range of a logarithmic function is (infinity, infinity). The logarithmic function graph passes through the point (1, 0), which is the inverse of (0, 1) for an exponential function. The graph of a logarithmic function has a vertical asymptote at x = 0.

4.3 - Properties of Logarithms Take the log of the argument divided by the log of the base. The log of a product is the sum of the logs. The log of a quotient is the difference of the logs. The exponent on the argument is the coefficient of the log.

A logarithm is just another way of writing exponents. Thus, the properties of logarithms are derived from the properties of exponents.There are 4 important logarithmic properties: log xy = log x + log y. log x/y = log x - log y. log am = m log a. logba = (log a)/(log b)

The most common types of logarithms are common logarithms, where the base is 10, binary logarithms, where the base is 2, and natural logarithms, where the base is e 2.71828.

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