Log Properties

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mathxyz

Junior Member
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Jul 8, 2005
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If LN 2 = a and LN 3 = b, use log properties to write each log in terms of a and b.

1) LN 2e

2) log_2 (3)

I request only the proper log properties. I do not want the answers. I need to learn logs before next week's test. I have it under control with the exception of certain questions.
 
Janet, what log properties are in your textbook? Perhaps you could use those?
 
Trying to understand. Is it possible you mean
If LN(a) = 2 and LN(b) = 3...
or do you have sometheng else in mind? LN = 2 doesn't mean anything.
-------------------
Gene
 
Gene

If natural log = 2 and natural log = 3, use log properties to write each log in terms of a and b.

1) natural log 2(e)

2) log_2 (3) READ: log of 2 times 3

I request only the proper log properties. I do not want the answers. I need to learn logs before next week's test. I have it under control with the exception of certain questions.
 
natural log = 2 and natural log = 3
Click to expand...

That's not any better. LN, or "natural log", is not a number. It does not equal 2, and it does not equal 3. It's a function.

ln(x) means "the exponent you put on e to get x".

log<sub>b</sub>(x) means "the exponent you put on b to get x"

ln is the same as log<sub>e</sub>.

2) log_2 (3) READ: log of 2 times 3
Click to expand...

No, that's read "the logarithm, with respect to base 2, of 3", or "log base 2 of 3" for shortness.
 
CORRECTION MADE

CORRECTION MADE:

I was able to solve a similar question using the rule given in the textbook.

LOOK:

If LN 2 = a and LN 3 = b, express log below in terms of a and b.

1) LN 6

LN 6 = LN (2 * 3) = LN 2 + LN 3 = a + b

I just don't know what log rule to use to solve the following:



2) LN 2(e)

3) log_2 (3) READ: log base 2 of 3 same as log base 2 TIMES 3

How do I express question 2 amd 3 in terms of a and b?
 
log base 2 of 3 same as log base 2 TIMES 3
Click to expand...

"TIMES" multiplies two things together. What two things are being multiplied together here?
 
Re: CORRECTION MADE

mathxyz said:
If LN 2 = a and LN 3 = b
Click to expand...
2) LN 2(e) = ln(2) + ln(e) = a + 1 -- 'e' is the base of the Natural Logarithms

3) log_2 (3) = ln(3)/ln(2) = b/a -- Any base will split it up, like that, but base 'e' seemed most convenient.
 
Just to reiterate.
ln(b) means natural log of b
e^(ln(b)) = b

log(b) means base 10 log of b
10^(log(b)) = b

ln_x(b) means ln of b to base x
log_x(b) means log of b to base x
They are computed as
ln(b)/ln(x) or
log(b)/log(x) and they are the same 'cause
x^(ln_x(b)) = x^(log(b)) = b

Please note how each of them are typed. Including the ()s. They show where things end. If you type log a / b it can be confused.
log(a)/b or
log(a/b)
 
Yes...

It makes sense now. I will go back to the math book and practice more similar questions.
 
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