### Author Topic: Properties of logarithms on the TI nspire  (Read 1468 times)

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#### Kyle Kelly

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##### Properties of logarithms on the TI nspire
« on: April 10, 2019, 06:10:36 am »
Is it possible to make the TI-nspire apply properties of logarithms in order to rewrite multiple logs as one (the sum) or rewriting one log as multiple logs (the difference)?

I would assume the CAS version would be able to do this but I can't for the life of me figure out how. Is the feature built in the calculator or would you have to program it?
« Last Edit: April 10, 2019, 06:15:41 am by Kyle Kelly »

#### Xeda112358

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##### Re: Properties of logarithms on the TI nspire
« Reply #1 on: April 10, 2019, 10:33:22 am »
I think the nspire can collapse multiple logs into one (normal behavior), but extracting you'd have to program it yourself. If it is just integer inputs, you can use one of the nspire's factor() commands to factor the number and then manually construct a sum of logs.

#### Kyle Kelly

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##### Re: Properties of logarithms on the TI nspire
« Reply #2 on: April 10, 2019, 10:48:35 am »
I think the nspire can collapse multiple logs into one (normal behavior), but extracting you'd have to program it yourself. If it is just integer inputs, you can use one of the nspire's factor() commands to factor the number and then manually construct a sum of logs.

Okay to combine multiple logs into one how would i do it?

For example: 5 log base 3(y) - log base 3(x-4)

https://imgur.com/a/Cxvkuax picture for reference and the solution i'm trying to get

#### Xeda112358

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##### Re: Properties of logarithms on the TI nspire
« Reply #3 on: April 10, 2019, 11:33:28 am »
Oh, I just tested it out on my calc and it didn't simplify :|

What did work is when I did:
Code: [Select]
log(3^(5*log(y,3)-log(x-4,3)),3)