Adjust answer in LOG

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Aug 6th, 2022
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How to adjust answer in LOG

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in this lesson weamp;#39;re going to talk about evaluating logs using the change of base formula so we know that log base 2 of 16 is equal to 4 because 2 to the fourth power is 16. but letamp;#39;s say if you donamp;#39;t know that hereamp;#39;s how you can use the change of base formula to get the same answer but hereamp;#39;s the formula log base a of b is equal to log of b divided by log of a and the reason why itamp;#39;s called the change of base formula is because you can change the base originally the base is a but you can make it into any new base weamp;#39;ll call it c c could be 5 8 12. as long as these two are the same it doesnamp;#39;t really matter what c is the equation will work so log base 2 of 16 you can type it in your calculator as log 16 divided by log 2. now when you type it in your calculator like this itamp;#39;s automatically going to make it base 10. so regardless of whatever the new base is you will still get the right answer so go ahead and type that

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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.
The change of base formula is taking log of the argument number divided by the log of the base number, or you taking the ln of the argument number divided by the ln of the base number.
The change of base formula says logb b a = [logc c a] / [logc c b]. It means to change the base of a logarithm logb b a, we just use division [log a] / [log b] where these logarithms can have any (same) positive number as a base.
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)
Logarithms typically use a base of 10 (although it can be a different value, which will be specified), while natural logs will always use a base of e. If you need to convert between logarithms and natural logs, use the following two equations: log10(x) = ln(x) / ln(10) ln(x) = log10(x) / log10(e)
To change the base of a log you will take either the log of the argument number divided by the log of the base number, or you will take the ln of the argument number divided by the ln of the base number.
0:16 2:38 You can type it in your calculator as log 16 divided by log 2.. Now when you type it in yourMoreYou can type it in your calculator as log 16 divided by log 2.. Now when you type it in your calculator like this its automatically going to make it base 10.. So regardless of whatever the new base.
How do you solve logarithms step by step? If the unknown is outside the log, then evaluate the log. Most logs need a calculator to evaluate. If the unknown is inside the log, convert to exponential form. If there are multiple logs in an equation, try to combine as many as possible.

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