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#1 2008-12-11 02:48:31

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Logarithms - High school Level

#1. Evaluate

.

#2. If

, find the value of x.

#3. Evaluate :

.

#4. Simpligy:-

#5. Find the value of x which satisfies the relation

#6. Simplify:-

#7. If

, find the number of digits in
.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#2 2008-12-19 13:44:19

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Logarithms - High school Level

1.
7^x=1/343
7^x=7^-3
x=-3
2.
root8^x=10/3
x=2log(10/3)
    -------------
    3log(2)
x=1.12
3. I'm assuming you use a calculator, I've never encountered a question like that non-tech.
=2/3
Thats all I got so far:)


"If your going through hell, keep going."

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#3 2008-12-19 16:48:39

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Logarithms - High school Level

glenn101,
Solution to the first problem is correct, Good!
Here I have solved two problems for you:-


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2008-12-20 01:29:46

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Logarithms - High school Level

I shall do #2 and #3 for you, glenn101!

#2. If

, find the value of x.






x = 32.

#3. Evaluate :

.
=

=

=


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#5 2008-12-20 17:47:21

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Logarithms - High school Level

Thanks for the answers ganesh!
I havn't been taught those sorts of logs before, with surds and same bases.
Looks interesting.
Thanks againup


"If your going through hell, keep going."

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#6 2008-12-21 04:49:04

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: Logarithms - High school Level

glenn have you been taught change of base formula yet?
For number #3 ganesh used that.

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#7 2008-12-21 13:57:47

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Logarithms - High school Level

and no I havn't careless, I've only been taught how to deal with same bases, nothing advanced. Next year we deal with e and I'm guessing we will also be taught the change of base formula.


"If your going through hell, keep going."

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#8 2008-12-22 01:54:58

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Logarithms - High school Level

glenn101,

The base change formula is very useful.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#9 2008-12-22 12:59:54

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: Logarithms - High school Level

Ganesh i havent been taught that far yet... but for me the base change formula is using base 10 so we can use calculators...

so i always do this:

log 25 (100) = log 10 (100) * log 10 (25)

so always base 10.
but i can see what you mean by that formula and example.

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#10 2008-12-22 13:05:22

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Logarithms - High school Level

Hmm that formula looks straightforward and useful!
thanks for that ganesh!up


"If your going through hell, keep going."

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#11 2008-12-22 16:09:47

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,956

Re: Logarithms - High school Level

Its a pleasure helping you with logarithms,
logs are such an important tool in calculations!
For my Practical Final-I at University, I had to find the Young's Modulus and this would have been extremely difficult without logarithms or a scientific calculator! We were not allowed to use calculators!


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#12 2008-12-22 16:11:49

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: Logarithms - High school Level

Yup my pre-calculus class is heading there...NO CALCULATORS!
except the one in my head! tongue

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#13 2008-12-22 17:06:56

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Logarithms - High school Level

Yeah, logs have always been my favorite topic, its easy for me to understand.
Then comes calculus and trig.:D


"If your going through hell, keep going."

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