Latest CSC Aptitude Question SOLUTION: Find the value of x which satisfies the relation Log10 3+log10 (4x+1)=log10 (x+1)+1

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(#M40013481) CSC Logical Reasoning question Keep an EYE

Find the value of x which satisfies the relation
Log10 3+log10 (4x+1)=log10 (x+1)+1

Asked In CSC phani nagendra (11 years ago)

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phani nagendra  (11 years ago)

log10 3+log10 (4x+1)=log10 (x+1)+1
Log10 3+log10 (4x+1)=log10 (x+1)+log10 10
Log10 (3(4x+1))=log10 (10(x+1))
=3(4x+1)=10(x+1)=12x+3
=10x+10
=2x=7=x=7/2

Is this solution Helpfull? Yes (35) | No (2)  

sasi  (11 years ago)

10 is base==>>3(4x+1)=10(x+1)==>x=7/2

Is this solution Helpfull? Yes (6) | No   

Ankit agarwal  (11 years ago)

[log10a + log10b = log10 ab]
and also 1 can be written as log10 10,
so question can be rewritten as: log10 (3(4x+1))=log10(10(x+1)),
this can be solved to get 12x+3=10x+10,
that gives x=7/2=3.5

Is this solution Helpfull? Yes (4) | No (1)  

rani.m  (11 years ago)

we know that loge e=1, so log10 10 =1
then it becomes Log10 3+log10 (4x+1)=log10 (x+1)+log10 10
log10 3 - log10 10=log10 (x+1)-log10 (4x+1)
we know loga-logb =log(a/b)
then log(3/10) 10= log(x+1/4x+1)10
when bases are equal we can equate its powers
then 3/10=x+1/4x+1
12x+3=10x+10
2x=7
x=7/3

Is this solution Helpfull? Yes (1) | No (7)  

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