Can you distribute logarithms?

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Discussion Overview

The discussion centers around the question of whether the logarithm can be distributed over addition, specifically examining the expression logb (x + y) = logb x + logb y. Participants explore this concept through examples and counterexamples, engaging in both theoretical reasoning and practical testing of logarithmic properties.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the validity of the expression logb (x + y) = logb x + logb y, suggesting it may not hold true.
  • Another participant proposes testing the equation with specific values, indicating a willingness to explore the claim through practical examples.
  • A participant reports successful tests with specific logarithmic values, initially concluding that the distribution works, but later acknowledges a misunderstanding of the logarithmic properties.
  • Several participants clarify that the logarithmic product rule, log(xy) = log(x) + log(y), is valid, contrasting it with the disputed addition case.
  • There is a discussion about the logarithm of specific numbers, such as log(1) and log(2), with one participant providing approximate values.
  • One participant expresses regret for a previous assertion about distributing logs, admitting to a mistake in their reasoning.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the original question. There are multiple competing views regarding the validity of distributing logarithms, with some participants initially supporting the idea before recognizing the error in reasoning.

Contextual Notes

Some participants' claims depend on specific examples, and there is a lack of clarity regarding the conditions under which the logarithmic properties apply. The discussion includes unresolved mathematical steps and assumptions about the properties of logarithms.

mileena
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Does anyone know if the following is true:

logb (x + y) = logb x + logb y

Thanks. This isn't homework, but I am just wondering if the following is true. I already know the logarithm product, quotient, and power rules!
 
Last edited:
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Why don't you try to find a counterexample?
 
Ok, good idea. I don't know how to use a scientific calculator yet to figure out logs, but I know they are online. I will plug in some real numbers to see if the equation s true or not.
 
Ok, I just did, using log 2 and log 3, and then again with log 8 and log 10. It worked! you can distribute logs!

Thanks, and sorry for posting so many questions in one day.
 
mileena said:
Ok, I just did, using log 2 and log 3, and then again with log 8 and log 10. It worked! you can distribute logs!

Thanks, and sorry for posting so many questions in one day.

It shouldn't work :confused:

Can you post what you did?
 
:redface:
 
log(2)=log(1+1)=log(1)+log(1)

Is this true?
 
johnqwertyful said:
log(2)=log(1+1)=log(1)+log(1)

Is this true?

What's the log of 1?
What's the log of 2?
 
Nugatory said:
What's the log of 1?
What's the log of 2?

I think he knows lol. He just asked it to the OP :-p
 
  • #10
micromass said:
I think he knows lol. He just asked it to the OP :-p

Oops - right you are. Sorry about that.
 
  • #11
mileena said:
Does anyone know if the following is true:

logb (x + y) = logb x + logb y

Thanks. This isn't homework, but I am just wondering if the following is true. I already know the logarithm product, quotient, and power rules!


Make and test an example. Imagine your base is 10, and x=100 and y=10,000,000.

log10(100+10000000)=log10(100)+log10(10000000)
Does this make sense? Does this not make sense?
 
  • #12
Log(xy) = log(x) + log(y). Unless xy = x+y, your equation is wrong.
 
  • #13
Hi, sorry for not posting sooner, but I was busy all day and I don't really have Internet access until I get to the library.

Let me also say that I am an idiot!

Yesterday, I said that you could distribute logs, so that:

logb (x + y) = logb (x) + logb (y)

But I made a mistake. Instead of adding, for example, 2 and 3, and taking the log of 5 and comparing that with the sum of log 2 and log 3, I multiplied 2 and 3! Thus I got:

logb x + logb y = logb (xy)

which is, of course, the product rule.
 
  • #14
symbolipoint said:
Make and test an example. Imagine your base is 10, and x=100 and y=10,000,000.

log10(100+10000000)=log10(100)+log10(10000000)
Does this make sense? Does this not make sense?

mathman said:
Log(xy) = log(x) + log(y). Unless xy = x+y, your equation is wrong.

I did not say that the equation was correct. I only presented it, and then asked two questions. I know already that the equation is wrong. mileena already found understanding that was sought.
 
  • #15
@symbolipoint: I think mathman may have been responding to the original post when he was commenting.

@Nugatory: log 1 = 0 and log 2 ≈ 0.6931...

-Junaid :-p
 
  • #16
junaid314159 said:
@symbolipoint: I think mathman may have been responding to the original post when he was commenting.

@Nugatory: log 1 = 0 and log 2 ≈ 0.6931...

-Junaid :-p

mathman, that is possible. I inferred that you may have responded to my post because yours came directly after it, and other interrelations of responses of posts were not clear.

I tried to give an example to be checked and asked if the example made sense.
 
  • #17
symbolipoint said:
mathman, that is possible. I inferred that you may have responded to my post because yours came directly after it, and other interrelations of responses of posts were not clear.

I tried to give an example to be checked and asked if the example made sense.

I was responding to the original post.
 

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