Aptitude - Logarithm - Discussion
Discussion Forum : Logarithm - General Questions (Q.No. 9)
9.
If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Answer: Option
Explanation:
log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
log10 [5 (5x + 1)] = log10 [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9
x = 3.
Discussion:
14 comments Page 1 of 2.
Mehdi said:
9 years ago
What are we doing in step 3: 5(5x+1) = 10(x+5) and in step 4: 5x+1 = 2x+10.
Mehmood Ali said:
9 years ago
Explanation:.
log10 5 + log10 (5x+1) = log10 (x+5)+1.
log10 5 + log10 (5x+1) = log10 (x+5)+log10 10.
Therefore, log10 a + log10 b = log10 (a*b).
So, log10 [5(5x+1)] = log10 [10(x+5)].
Lets take values out of log10 to get the value of x;
5(5x+1) = 10(x+5).
25x+5 = 10x+50.
Re-arrange the values,
25x-10x = 50-5.
15x = 45.
x = 45/15.
(Now, 15*3 = 45).
x = 3.
log10 5 + log10 (5x+1) = log10 (x+5)+1.
log10 5 + log10 (5x+1) = log10 (x+5)+log10 10.
Therefore, log10 a + log10 b = log10 (a*b).
So, log10 [5(5x+1)] = log10 [10(x+5)].
Lets take values out of log10 to get the value of x;
5(5x+1) = 10(x+5).
25x+5 = 10x+50.
Re-arrange the values,
25x-10x = 50-5.
15x = 45.
x = 45/15.
(Now, 15*3 = 45).
x = 3.
Mahesh said:
8 years ago
Anyone please explain that step:2 log10 5 + log10 (5x+1) = log10 (x+5) + log10 10.
How is come?
How is come?
Abdur Rafay said:
7 years ago
How the 1 turned into log10 10? Please explain.
Bhavya said:
7 years ago
Log10 10=1 so place of1 they take log10 10.
Sharmi said:
7 years ago
Logx x =1 (it's one of the property).
So, log10 10=1.
Inorder to find x, 1 is being replaced with log10 10.
So, log10 10=1.
Inorder to find x, 1 is being replaced with log10 10.
Ashmi said:
7 years ago
How logx x=1?
Saim said:
6 years ago
It's solved wrongly. Because log2^2 or log4^4 is also equal to 1. If we put these in replace of one the answer is wrong.
Correct me, if I am wrong.
Correct me, if I am wrong.
Biswa said:
5 years ago
I want to all formula & explanation about logarithms?
Devota said:
4 years ago
I'm not getting this, please anyone explain in detail.
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