CAS Simplify(log10) always changes to LN
06-21-2018, 06:50 PM
Post: #1
 scropsey Junior Member Posts: 2 Joined: Jun 2018
CAS Simplify(log10) always changes to LN
Is there a way to have the CAS simplify result in the base that is used?

Every expression I have tried changes the base to LN.

Example: simplify ( log10(2) + log10(6) ) results in (LN(2) + LN(6))/(LN(2) + LN(5))

I am looking to use it as a way to introduce/reinforce the properties of logs.
06-22-2018, 11:15 AM (This post was last modified: 06-22-2018 02:40 PM by DrD.)
Post: #2
 DrD Senior Member Posts: 1,133 Joined: Feb 2014
RE: CAS Simplify(log10) always changes to LN
(06-21-2018 06:50 PM)scropsey Wrote:  Is there a way to have the CAS simplify result in the base that is used?

Every expression I have tried changes the base to LN.

Example: simplify ( log10(2) + log10(6) ) results in (LN(2) + LN(6))/(LN(2) + LN(5))

I am looking to use it as a way to introduce/reinforce the properties of logs.

Using the approx() command:

Number format: FIXED 2
approx(LOG(2)+LOG(6)); // ==> 1.08
approx(((2*ln(2)+ln(3))/(ln(2)+ln(5)))); // ==> 1.08
alog10(1.08); // ==> 12 (Using Ans1 as argument)

[CAS]
approx(log10(2)+log10(6)); // ==> 1.08
alog10(1.08); // ==> 12 (Using Ans1 as argument)

-Dale-
06-22-2018, 12:02 PM
Post: #3
 Marcel Member Posts: 176 Joined: Mar 2014
RE: CAS Simplify(log10) always changes to LN
Hi scropsey!
The Ti-Nspire CX CAS give the answser in base 10.
Marcel

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06-22-2018, 05:43 PM
Post: #4
 Carsen Member Posts: 206 Joined: Jan 2017
RE: CAS Simplify(log10) always changes to LN
I tackled this with using the Simplify command. Then I used LNCOLLECT to simplify it even further. The final result is LN(12)/LN(10). And since LOG(A)/LOG(B) or LN(A)/LN(B) = LOG of A with a base of B, you can easily read that the answer is the LOG of 12 with a base of 10. See the screenshot below.

As for why it goes to LN, I do not know why. And I am not knowledgeable enough to help you on how to get the answer in LOG form. Good luck and Happy Priming!

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06-25-2018, 06:19 AM (This post was last modified: 06-25-2018 06:19 AM by Stevetuc.)
Post: #5
 Stevetuc Senior Member Posts: 312 Joined: Jan 2014
RE: CAS Simplify(log10) always changes to LN
(06-21-2018 06:50 PM)scropsey Wrote:  Is there a way to have the CAS simplify result in the base that is used?

Every expression I have tried changes the base to LN.

Example: simplify ( log10(2) + log10(6) ) results in (LN(2) + LN(6))/(LN(2) + LN(5))

I am looking to use it as a way to introduce/reinforce the properties of logs.

It does seem to be deficient if not a bug that it simplifies by converting log10 to ln.

Until this is fixed, you can show the log properties more directly if you work in natural logs

Ie simplify(ln(2)+ln(6)) results in ln(12)

It really should be able to do the same for log10 though!
06-25-2018, 11:35 AM (This post was last modified: 06-25-2018 11:38 AM by Tim Wessman.)
Post: #6
 Tim Wessman Senior Member Posts: 2,293 Joined: Dec 2013
RE: CAS Simplify(log10) always changes to LN
Nearly all more advanced CAS systems do not have implemented a base 10 and use a natural log for everything. In fact, they all just call it "log". The Prime CAS follows that convention and we had to do work to get "log" renamed to "ln" for the cas and "log10" lowercase as a base 10.

"log10" is implemented as a purely numeric command on the CAS side as the concept doesn't have the concept of log in anything BUT e (which is the standard as I mentioned). It doesn't have a symbolic equivalent.

Personally, I'd love it were it to be handled better but that depends on someone encouraging the CAS author to do it!

TW

Although I work for HP, the views and opinions I post here are my own.
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