Can you distribute logarithms?

[mileena]

Does anyone know if the following is true:

log_b (x + y) = log_b x + log_b 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!

 

[micromass]

Why don't you try to find a counterexample?

 

[mileena]

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.

 

[mileena]

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.

 

[micromass]

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

Can you post what you did?

 

[junaid314159]

 

[johnqwertyful]

log(2)=log(1+1)=log(1)+log(1)

Is this true?

 

[Nugatory]

log(2)=log(1+1)=log(1)+log(1)

Is this true?

What's the log of 1?
What's the log of 2?

 

[micromass]

What's the log of 1?
What's the log of 2?

I think he knows lol. He just asked it to the OP :tongue:

 

[Nugatory]

I think he knows lol. He just asked it to the OP :tongue:

Oops - right you are. Sorry about that.

 

[symbolipoint]

Does anyone know if the following is true:

log_b (x + y) = log_b x + log_b 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?

 

[mathman]

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

 

[mileena]

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:

log_b (x + y) = log_b (x) + log_b (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:

log_b x + log_b y = log_b (xy)

which is, of course, the product rule.

 

[symbolipoint]

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?

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.

 

[junaid314159]

@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 :tongue:

 

[symbolipoint]

@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 :tongue:

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.

 

[mathman]

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.