Logarithms

Updated: 5/16/2020

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- y=a^x <-> x=loga(y)
- The base goes down. Note that a>0, a≠1. Remember your laws of indices as you will need to know how to convert.
- log=log10ln=lne
- Laws of Logarithm:1) loga(xy)=loga(x)+loga(y)2) loga(x/y)=loga(x)-loga(y)3) loga(x^r)=(r)loga(x)
- You can only combine when they have the same base. If there is a number in front of the log, change it into the power before continuing.
- Note: loga(a)=1a^loga(x)=x
- Ms Latha introduces Logarithms to 3 Loyalty.
- loga(b)=logc(b)/logc(a)
- This is how you change the base of Logarithms. You need to know this as your calculator can only calculate lne or log10.
- Ms Latha teaches the class how to use the calculator.
- e^x=2ln both sides, lne^x=ln2x=ln2
- ln both sides to cancel the e or log both sides but you can only do this when both sides have 1 term.
- The Laws of Logarithm are important when you do problems related to logarithms.
- e^2x=3e^x+4Let y=e^x, y^2=3y+4..y=4 or -1e^x=4lne^x=ln4
- When you have more than 1 term on 1 side and you are unable to ln/log, you can substitute an unknown for 'y'
- Changing of base of Logarithms
- If there is an e, it's encouraged to ln while if it's a number, it is encouraged to log.
- Solving problem sums, you need to learn to solve it smartly and use your knowledge of algebra to help you. Thank you for coming to class today!