Alevels maths C2 help doubt question in text book logarithm and exponential

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Sena5
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#1
Report Thread starter 7 years ago
#1
In C2 MATHEMATICS IN LOGARITHMS AND EXPONENTIALS,

a) in 3F exercise,
the question is

Solve giving answer to 3 significant figures
log x + log x = 2
2 4

How to solve this? Can u show the steps?

Another question is in 3G
given that p= log 16, express in terms of p.
q

i) log 2 (ii) log (8q)
q q

Pls help. Sir and please add me on your friends contacts. I am private student. Therefore i need to ask doubts ,where i found ur profile helpful to clear my doubts. All these questions are from logarithms and exponentials.

thank u
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TenOfThem
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#2
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#2
(Original post by kers123)
In C2 MATHEMATICS IN LOGARITHMS AND EXPONENTIALS,

a) in 3F exercise,
the question is

Solve giving answer to 3 significant figures
log x + log x = 2
2 4

How to solve this? Can u show the steps?

Another question is in 3G
given that p= log 16, express in terms of p.
q

i) log 2 (ii) log (8q)
q q

Pls help. Sir and please add me on your friends contacts. I am private student. Therefore i need to ask doubts ,where i found ur profile helpful to clear my doubts. All these questions are from logarithms and exponentials.

thank u
You may find LaTex useful

I assume that your question is

\log_2x + \log_4x = 2

Do you know how to change base so that both elements of the LHS have the same base
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Sena5
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#3
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#3
i did like this.

Image

(log x + log x )
10 10
------ -------- = 2
log 2 log 4
10 10

2= 2log x
10
--------------------
log 2 + log 4
10 10

log x = 0.9
10

0.9
10 =x

therefore x= 8

but the answer behind the book is 2.52
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username1042689
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#4
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#4
 log_2x + log_4x = 2

1.) Use the change of base rule to change log_4x into something to base 2

2.) then use  log_axy = log_ax + log_ay

3.) then solve  log_axy = 2
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Sena5
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#5
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#5
cool but how to change base 4 to 2. have any idea?
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TenOfThem
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#6
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#6
(Original post by kers123)
cool but how to change base 4 to 2. have any idea?
\log_4x = p gives x = 4^p = 2^{2p} so that \log_2x = 2p = 2\log_4x
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