Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

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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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.

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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"If your going through hell, keep going."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

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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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.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

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.

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 again

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"If your going through hell, keep going."

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.

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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"If your going through hell, keep going."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

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.

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.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Logarithms - High school Level

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

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"If your going through hell, keep going."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,179

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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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.

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!

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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"If your going through hell, keep going."