The log of 1000, it returns log base10=3 because 10x10x10 is equal to 1000.
If the log is something with a lot decimals like 2.302585, how should I do the math?
Also how you use the calculator to change the base of log10?
Scientific calculators will have two logarithm buttons. Log is traditionally base-10 and ln is base-e.
If you need to do a calculation using a different base, like base-2, you can use the process discussed in the lecture to convert things.
Unfortunately, calculating the log of decimal numbers is a little out of scope for this course.
For rational numbers, you need to work with the calculation in exponential form and then do a lot of messing about.
For irrational numbers, one common approach is to use a Taylor series to approximate the answer to the level of precision you need.
Personally, I’d recommend just using a calculator to find the answer as performing the required calculations by hand can be incredibly tedious and time consuming.
That may sound like a bit of a cop-out but prior to the invention of calculators, people would use slide rules and log books to try and make life easier - so you’re definitely not alone when it comes to using shortcuts for your log calculations!
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thank you the the reply, I think I understand better now.
Using log with base 10 seems a lot more easy for me, is there any utility about using base-e?
The common log (base-10) is a bit easier to wrap your head around when first learning logarithms but the natural logs are very widely used, especially when you’re dealing with things like exponential growth.
As you become familiar with more advanced math topics, you’ll frequently start seeing things like e^x showing up. In those cases working with the natural log is the obvious choice.
In computer science you tend to see a lot of binary numbers, so working with the binary log (base-2) can be very handy. Unfortunately calculators still don’t offer this base as a default option (much to my annoyance!) so learning the “change of base” rule can definitely serve you well.
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