Manipulate numbers log easily

Aug 6th, 2022
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How to manipulate numbers log

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eight in this class were gonna do a lot of manipulation of logarithms and exponential functions okay and some of these relationships were going to use a lot throughout the semester and what I want to do is help you understand them by applying them to some very simple applications so here I have a to the M times a to the N equals a to the M plus N okay this works for any base you might use the base e for natural logs you might use base 10 and then if you just have a log and you dont put the base below it youre in fine log base 10 so lets apply this is something we can understand okay I think everybody this room could do a hundred times a thousand so I could say ten squared times 10 cubed is equal to ten to the two plus three now lets check that out okay Im 10 squared is a hundred ten cubed is a thousand and ten to the two plus three is ten to the fifth which with five zeros is a hundred thousand in a hundred times a thousand is a hundred thousand now if I come and express this i

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0:28 1:02 Going into math. We can see straight away log to base a of B. So we can do log base 2 of 32. AndMoreGoing into math. We can see straight away log to base a of B. So we can do log base 2 of 32. And theres our answer.
We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.
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.
We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.
An antilogarithm, or antilog, performs the inverse operation of the logarithmic function.
Answer and Explanation: A logarithm with base 10 is denoted as log(x), and it is called the common logarithm. To convert a logarithm, logb (x) to base 10, we can use our change of base formula as follows: logb(x)=log10(x)log10(b)=log(x)log(b)
The change of base formula also works with the natural logarithm, ln. To change the base of a logarithm to a natural logarithm, use the formula: loga(b)=ln(b)/ln(a).
Explanation: In order to eliminate the log based ten, we will need to raise both sides as the exponents using the base of ten. The ten and log based ten will cancel, leaving just the power on the left side.
Answer and Explanation: The inverse of log10 (x), denoted log(x), is 10x. In general, we have the following rule regarding the inverse function of a logarithmic function. If f(x) = logb (x), then f-1 (x) = bx.
The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number. The power to which the base e (e = 2.718281828.) must be raised to obtain a number is called the natural logarithm (ln) of the number. NumberExponential ExpressionLogarithm1/1000 = 0.00110-3-36 more rows

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