# C2 Log question

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#1
Stuck with this:

Find the solution

(2^x)(2^x+1) = 10

Thanks

Slightly stuck with another question too:

Write log10(x+4) - 2log10(x)+log10(x+16) as a single log

Without a calculator show x=4 is a root log10(x+4) - 2log10(x)+log10(x+16)
0
6 years ago
#2
(Original post by Sam160)
Stuck with this:

Find the solution

(2^x)(2^x+1) = 10

Thanks
Can you clarify which of these is the problem

or

0
6 years ago
#3
(x^a)(x^b) = x^(a+b)
0
6 years ago
#4
(Original post by Sam160)
Stuck with this:

Find the solution

(2^x)(2^x+1) = 10

Thanks
(Original post by StrangeBanana)
(x^a)(x^b) = x^(a+b)
This
0
#5
(Original post by TenOfThem)
Can you clarify which of these is the problem

or

The 2nd one, thanks for the help guys
0
6 years ago
#6
(Original post by Sam160)
Stuck with this:

Find the solution

(2^x)(2^x+1) = 10

Thanks
If it is

I got x = 1.16 (3sf)

Log all sides so

Log (2^x) (Log 2^x+1) = Log 10

Log (2^x * 2^x+1 ) = Log 10

Log (2^2x +1) = 1 (Log 10 = 1)

(2x+1)Log 2 = 1
(2x + 1) = 1 / Log 2
rearranging gives x = 1.160964047 which is 1.16(3sf)

NOTE: I have just recently learnt this topic so please confirm to me whether my answer is right or if you dont have the mark scheme. Other people should attempt the question to confirm my answer or disapprove :/
1
#7
(Original post by AhmedDavid)
If it is

I got x = 1.16 (3sf)

Log all sides so

Log (2^x) (Log 2^x+1) = Log 10

Log (2^x * 2^x+1 ) = Log 10

Log (2^2x +1) = 1 (Log 10 = 1)

(2x+1)Log 2 = 1
(2x + 1) = 1 / Log 2
rearranging gives x = 1.160964047 which is 1.16(3sf)

NOTE: I have just recently learnt this topic so please confirm to me whether my answer is right or if you dont have the mark scheme. Other people should attempt the question to confirm my answer or disapprove :/
That is what i have got now too, thanks for your help!
0
6 years ago
#8
(Original post by AhmedDavid)
If it is

I got x = 1.16 (3sf)

Log all sides so

Log (2^x) (Log 2^x+1) = Log 10

Log (2^x * 2^x+1 ) = Log 10

Log (2^2x +1) = 1 (Log 10 = 1)

(2x+1)Log 2 = 1
(2x + 1) = 1 / Log 2
rearranging gives x = 1.160964047 which is 1.16(3sf)

NOTE: I have just recently learnt this topic so please confirm to me whether my answer is right or if you dont have the mark scheme. Other people should attempt the question to confirm my answer or disapprove :/
Your method is correct and just remember to ALWAYS work in a logical and methodical manner. Many people make mistakes when they try to do too much in their heads!
0
#9
Slightly stuck with another question too:

Write log10(x+4) - 2log10(x)+log10(x+16) as a single log

Without a calculator show x=4 is a root log10(x+4) - 2log10(x)+log10(x+16)
0
6 years ago
#10
(Original post by Sam160)
Slightly stuck with another question too:

Write log10(x+4) - 2log10(x)+log10(x+16) as a single log

Without a calculator show x=4 is a root log10(x+4) - 2log10(x)+log10(x+16)

alog(b)=log(b^a)
log(a)+log(b)=log(ab)
log(a)-log(b)=log(a/b)
0
#11
(Original post by CJG21)

alog(b)=log(b^a)
log(a)+log(b)=log(ab)
log(a)-log(b)=log(a/b)
I have an answer for the first question which i know is wrong from the 2nd which is the problem
0
6 years ago
#12
(Original post by Sam160)
I have an answer for the first question which i know is wrong from the 2nd which is the problem
0
#13
(Original post by CJG21)
Nevermind i've worked out both
0
6 years ago
#14
(Original post by Sam160)
I got to log10[(x+4)/x^2] + log10(x+16) but going wrong after
Well you can use your log laws to simplify that to one log.

Spoiler:
Show
log[(x+4)(x+16)/x^2]
1
6 years ago
#15
(Original post by Sam160)
Nevermind i've worked out both
Excellent.
0
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