Modify side in LOG

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Aug 6th, 2022
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How to modify side in LOG

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in this video what I want to do is show you how to evaluate a logarithmic expression when the bases are not the same so on a problem like this a lot of you might look at this immediately just kind of give up like the bases are not the same you canamp;#39;t apply the rules of logarithms or the properties of logarithms right and I think one of the first things we always do in class like when weamp;#39;re giving you the notes you know as a teacher like hereamp;#39;s all you know itamp;#39;s like one thing I always like tell my students like you can only apply the properties of logarithms when the bases are the same you know thatamp;#39;s especially when weamp;#39;re looking at the product and the you know quotient properties and stuff like that you know one thing I kind of recognize with this one or at least when Iamp;#39;m looking at this this isnamp;#39;t like the product like remember the product represents like two separate logarithms that are separated by addition right then

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The names of these rules are: Product rule. Division rule. Power rule/Exponential Rule. Change of base rule. Base switch rule. Derivative of log. Integral of log.
The Three Basic Log Rules: 1) Product Rule: logb(mn) = logb(m) + logb(n) 2) Quotient Rule: logb(m/n) = logb(m) logb(n) 3) Power Rule: logb(mn) = n logb(m)
The logarithmic form logaN=x l o g a N = x can be easily transformed into exponential form as ax=N a x = N . Generally, large astronomical and scientific calculations are expressed in exponential form, and here we can use the log to exponential form of transformation.
To reverse a log base 10, you can use the following equation: 10^log(x) = x. This equation states that raising 10 to the power of the log of a number (x) will result in the original number (x).
4:05 6:34 So. We can apply on the right side. And get it to have the same base as the left side. So. If weMoreSo. We can apply on the right side. And get it to have the same base as the left side. So. If we change the base to 2 we get log base 2 of hex plus 6 divided by log base 2 of 8.
0:45 3:20 Both sides using base B. Now exponential functions in logarithmic functions these are inverses asMoreBoth sides using base B. Now exponential functions in logarithmic functions these are inverses as long as the bases are the same. Theyre going to undo one another.
Suppose that x0 is some number, and log4x=y. That means that 4y=x. Now 4=22, so x=4y=(22)y=22y, and that means that log2x=2y.
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. Change the negative exponent into a fraction on the right side.

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