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Aug 6th, 2022
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How to Cancel state in LOG

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Hello again. Were still looking at logarhythms, and this time were looking at a very important rule, an idea of kind of like cancelling it out. Weve looked at that in previous modules. Cancelling to like, get a variable say, on its own. In this case, what we have is log to the base 4 of 4 to the 8. Well, the nice thing here is, what is a logarhythms? Well, its asking us to figure out what does the base have to be put to in order to get the term in say the brackets I just put in. so what does 4 have to be raised to, or put -- what power does it have to be put to become 4 to the 8? Well, if we think about it, thats kind of there in the answer. What does 4 have to be put through to get to be 4 to the power of 8? Well, 8. So this can merely be thought of as 8. And you think, if you have the base and the number here are the same, all thats left is the exponent. In fact, we can apply that power rule and rewrite this as 8 log 4 of 4. Well what does 4 need to be raised to, to get 1?

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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)
ing to the rule of logs, a log of a base with similar bases will cancel, and will leave only the power.
The logarithms and exponentials cancel each other out (equation (4)), giving our product rule for logarithms, ln(xy)=ln(x)+ln(y).
ing to the rule of logs, a log of a base with similar bases will cancel, and will leave only the power.
The Four Basic Properties of Logs logb(xy) = logbx + logby. logb(x/y) = logbx - logby. logb(xn) = n logbx. logbx = logax / logab.
Recall that logs and exponents are inverses of each other, so they cancel each other out. 2) Example: log 8 x = 2 Since the base of the log is 8, we can undo (or cancel) the log by exponentiating it, or raising it to a power, with a matching base of 8.
If you have the same operation on both sides of an equation, they cancel each other out! Keep in mind that this only works when the logarithms on both sides of the equation have the same base. If you had a logarithm with base 3 on one side and a logarithm with base 7 on the other side, they wont cancel out.
Properties of Logarithms Logarithm Base Properties. Product Property. Quotient Property. Power rule. Change of Base rule. Reciprocal rule. Exponent law vs Logarithm law. Natural Logarithm properties.

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