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

ganesh
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Registered: 2005-06-28
Posts: 15,218

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
.


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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:)


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

ganesh
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Registered: 2005-06-28
Posts: 15,218

Re: Logarithms - High school Level

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


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

ganesh
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Registered: 2005-06-28
Posts: 15,218

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 :

.
=

=

=


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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


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

careless25
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Registered: 2008-07-24
Posts: 555

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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,218

Re: Logarithms - High school Level

glenn101,

The base change formula is very useful.


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

careless25
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Registered: 2008-07-24
Posts: 555

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


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

ganesh
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Registered: 2005-06-28
Posts: 15,218

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!


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

careless25
Real Member
Registered: 2008-07-24
Posts: 555

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


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