Hello slipery

The definition of a logarithm of a certain number is that power to which the base must be raised to give you the number. So:

If , then .

Can you see it now?

Grandad

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- Jan 8th 2009, 07:11 AM #1

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## Log question

Hey guys.. I am doing some correspondence work and I was wondering if I could have help with a question. Am I just supposed to do this by trial and error? Seems like there should be an easier way.

http://s180.photobucket.com/albums/x...=logquest2.jpg

Thanks

- Jan 8th 2009, 08:15 AM #2

- Jan 8th 2009, 08:19 AM #3

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Hi Slipery,

You can calculate that value using the following;

y = log7(12)

7^y = 12

y*ln(7) = ln(12)

y = ln(12)/ln(7)

Therefore, log7(12) = ln(12)/ln(7)

This is also known more generally as the 'Change of base formula'.

logA(B) = ln(B)/ln(A)

EDIT: I apologize, I misread the picture you linked - feel free to ignore me.

- Jan 8th 2009, 09:10 AM #4

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I don't think you misread my post Revenantus.

And I do understand what you're saying Grandad.

The method you laid out Revantus is the one that I would do myself. I am just wondering whether that is correct.

It is basically saying 7^ log7(12).

First I must figure out log 7(12), and then all I do is work that out as an exponenet for 7. Log 7(12) is what I am having trouble with. I am aware of how to use the scientific calculator to figure the answer out, but none of the examples I am given seem to come out in a decimal like that, so I am just wondering if that is indeed how I am supposed to solve the problem

- Jan 8th 2009, 09:21 AM #5

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Instead of just the mathematical notation, let's think through what each part means.

log7(12) means "The power I must raise 7 to in order to result in 12".

Therefore 7^log7(12) means "I raise 7 to the power that I must raise 7 to in order to result in 12"

- Jan 8th 2009, 09:28 AM #6

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- Jan 8th 2009, 09:32 AM #7

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- Jan 8th 2009, 09:35 AM #8

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- Jan 8th 2009, 09:38 AM #9

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Another approach would be to look back at the two definitions Grandad gave us.

a^x = y and x=loga(y)

By substituting loga(y) in place of x in the first definition we can form;

a^loga(y) = y

Your expression is of the same form as above, try plugging in the values and see what you get.

- Jan 8th 2009, 09:45 AM #10

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- Jan 8th 2009, 09:47 AM #11

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- Jan 8th 2009, 09:48 AM #12

- Jan 8th 2009, 10:09 AM #13