M4maths Previous Puzzles

15 Feb 2017 Log

If log4 + log(13x+1) = log(5x+9) + 1, then value of x is ?
Note: Assume all log represented above is to the base of 10.

OPtion

1) 15/8
2) 3
3) -43/4
4) 43/4
5) 86
6) -43
7) 43/2
8) 1
9) -43/2
10) None of these

Solution

Considering base is 10, so 1 could be represented as Log10
=> log4 + log(13x+1) = log(5x+9) + log10

Let’s revise the formula for Logs
Log(XY) = LogX+LogY
Applying the formula we get:
Log[4*(13x+1)] = Log[10*(5x+9)]
Solving
=> 52x + 4 = 50x + 90
=> 2x = 86
=> x = 43

Option 10)

Correct Option: 10 Best Solution (17)

G.S.Kantharao   8 years AGO

log4+ log(13x+1)=log (5x+9)+1
log4*(13x+1)=log(5x+9)+log10
log(52x+4)=log10*(5x+9)
log(52x+4)=log(50x+90)
52x+4=50x+90. (By removing log)
52x-50x= 90-4=86
2x=86
x=43
Hence the right choice is 10

Like? Yes (5) | No (1)  

Mukund Manohar   8 years AGO

log4 + log(13x+1) = log(5x+9) + 1
=> log4 + log(13x+1) = log(5x+9) + log10
=>log[4(13x+1)] = log[10(5x+9)]
=> 4(13x+1) = 10(5x+9)
=> 52x + 4 = 50x + 90
=> 2x = 86
=> x = 43
Value of x is 43

Like? Yes | No   

shashikanth reddy palla   8 years AGO

since loga +logb= logab
log4+log(13x+1)=log(4*(13x+1))»»1
log(5x+9)+1=log(5x+9)+log10 [since log10 =1 becoz base is 10]
log(5x+9)+log10=log(10*(5x+9))»»2
equate 1 and 2
log(4*(13x+1))=log(10*(5x+9))
4*(13x+1)=10*(5x+9)[logs are cancelled]
therfore x=43

Like? Yes (1) | No (1)  

Dr.Dipin Singh   8 years AGO

log4 + log(13x+1)= log (5x+9) +1
or log( 4*(13x+1))= Log (5x+9)+log 10 = log (10*(5x+9)
or log (52x+4)= log (50x+90)
or 52x+4= 50x+90
2x=86
x=43 ... none of given options

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PA . Mangaladeepa   8 years AGO

log(13x+1)-log(5x+9) = 1-0.6020
log(1-9)+log(13x-5x)=1-0.6020
log(8)+log(8x)=1-0.6020
log8x=1-0.6020-0.903
0.903x=0.505
x=-0.559246

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Amarnath Kumar Upadhyay   8 years AGO

log4*(13x+1)/log(5x+9)*10=log10
x=-1/2

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Sneha Dutta Roy   8 years AGO

answer is 43 , since 1 can be written as log 10 base 10. Then on simplifying we get 43

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B.Sharma   8 years AGO

log4*(13x+1)=log(5x+9)*10
52x+4=50x+90
2x=86
x=43

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Deepak Yadav   8 years AGO

using property, we get a equation-
4*(13x+1)= 10*(5x+9)
solving this we get x=43

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yamini velaga   8 years AGO

log ab =log a +log b
log (a÷b)= log a - log b

log{[4×(13x+1)]÷(5x+9)} = 1
(52x+4)÷(5x+9) = 10
52x+4 = 50x + 90
2x = 86
x = 43

Answer :(43)------ None of the above

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Rakesh   8 years AGO

log4+log(13x+1)=log(5x+9)+1
log 4*(13x+1)=log(5x+9)+1
log4*(13x+1)/5x+9=1
4*(13x+1)/(5x+9)=10
ans is 43
so none of these

Like? Yes | No (1)  

shilpa patel   8 years AGO

log(52x+4)=log(5x+9)+1 //logab=loga+logb
log([52x+4]/[5x+9])=1 //loga/b=loga-logb
[52x+4]/[5x+9]=10
52x+4=50x+90
so x=86/2
x=43

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Pragati Rode   8 years AGO

log4+log(13x+1) -log(5x+9) = 1
log(4*(13x+1)) -log(5x+9) = 1

log((52x+4)/(5x+9)) = 1
so base is 10
we get
10^1 = (52x+4)/(5x+9)
10(5x+9) = 52x +4
50x +90 = 52x +4
2x=90-4
2x=86
x=43
so option is 10

Like? Yes | No (1)  

Ajay Sharma   8 years AGO

log4+log(13x+1)=log(5x+9)+1
since log a+log b=log(a*b) & log10=1(since base is 10)
so log 4+log(13x+1)=log(5x+9)+log10
so log(52x+4)=log(50x+90)
log(52x+4)-log(50x+90)
log((52x+4)/(50x+90)=log1
so,(52x+4)/(50x+90)=1
52x+4=50x+90
x=43

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somveer   8 years AGO

Now, assume log base on 10 all of those above.
Log{4(13x+1)}=Log{(5x+9)10}
52x+4=50x+90
2x=86
x=43.

Like? Yes | No (1)  

sapana manjarekar   8 years AGO

log 4 + log (13x +1)=log (5x+9) +1
log(4(13x+1))-log(5x+9)=1
log((52×+4)/(5x+9))=1
(52x+4)/(5x+9)=10
52x+4=50x+90
2x=86
x=43

Like? Yes | No (1)  

sindhu   8 years AGO

log4+log(13x+1)=log(5x+9)+log10
4(13X+1)=(5x+9)*10
x=43

Like? Yes | No (1)