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#1 2008-12-12 19:50:52

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,189

Logarithms - High school - II

#1. What is the value of

?

#2. What is the value of

?

#3. What is the value of

?

#4. If

,
what is the value of x?

#5.What is the value of

?

#6. If

,

what is the value of x?

#7. If

,
then what is the value of
?

#8.What is the value of

?

#9.If

then

(1)


(2)

(3)

(4) None of these

#10. If log 2 = x, log 3 = y, and log 7 = z, then what is the value of

?

#11. If

,
then what is the value of x?

#12. What is the value of

?

#13. If

,
then what is the value of
?

#14. If log 27 = 1.431, what is the value of log 9?

#15. If

,
and

,

then what is the value of x?


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#2 2008-12-19 13:58:56

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

Re: Logarithms - High school - II

1.
2^x=16
2^x=2^4
=4
2.
343^x=7
343^x=343^1/3
=1/3
4.
x^-1/2=9/16
x^-1/2=256/81^-1/2
x=256/81

Last edited by glenn101 (2008-12-19 15:28:23)


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#3 2008-12-19 16:36:23

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,189

Re: Logarithms - High school - II

glenn101,
All correct! Very well done!!!


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#4 2008-12-19 17:38:05

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

Re: Logarithms - High school - II

3.
log sqrt(232)
= .5 log 232
= 1.183

5. log sqrt(8)/log 8
= 0.5 log 10 (8)/ log 10 (8)
= 1/2
i think..

6. log 32 x = 0.8
32 ^0.8 = x
16 = x

8.
a) log 5 (5) = 1

b) log4 (9)
= log 10 (9)/ log 10 (4)
= 1.585

c) log 3 (2)
= log 10 (2) / log 10 (3)
= 0.631

1 * 1.585 * 0.631 = 1.000

9.
a^x = b^y
a)y log a (b) = x
log a (b) = x/y
log 10 (b)/ log 10 (a) = x/y
b)x log b (a) = y
log b (a) = y/x
log 10 (a)/ log 10 (b) = y/x

so i think the right answer is (3)

12. 16 ^ (log 4 (5))
16 ^ (log 10 (5) / log 10 (4))
= careless25 :D

13. If log 10 (7) = a
then log 10 (1/70) = a - 2a - 1
= -1.8451

14.
if log 27 = 1.431
then log 9 = 1.431/1.5
log 9 = 0.954
because 9 ^ 1.5 = 27

15. same reasoning as above

if log 10 (3) = .477
then 1000^ x = 3
log 1000 (3) = x
log 1000 (3) = .477/3
x = .159
because 10 ^ 3 = 1000

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#5 2008-12-20 17:33:43

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,189

Re: Logarithms - High school - II

Well done, careless25!
wow_001.gif


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#6 2008-12-20 17:41:11

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

Re: Logarithms - High school - II

It's good to see other people attempting these questions:)
They are very helpful for revising my maths, thanks ganesh!up


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