Aptitude - Logarithm - Discussion

Discussion :: Logarithm - General Questions (Q.No.9)

9. 

If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

[A]. 1
[B]. 3
[C]. 5
[D]. 10

Answer: Option B

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.


Mehdi said: (Sep 13, 2015)  
What are we doing in step 3: 5(5x+1) = 10(x+5) and in step 4: 5x+1 = 2x+10.

Mehmood Ali said: (Oct 25, 2015)  
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.

Mahesh said: (Dec 31, 2016)  
Anyone please explain that step:2 log10 5 + log10 (5x+1) = log10 (x+5) + log10 10.
How is come?

Abdur Rafay said: (Jun 9, 2017)  
How the 1 turned into log10 10? Please explain.

Bhavya said: (Oct 22, 2017)  
Log10 10=1 so place of1 they take log10 10.

Sharmi said: (Dec 15, 2017)  
Logx x =1 (it's one of the property).
So, log10 10=1.
Inorder to find x, 1 is being replaced with log10 10.

Ashmi said: (Dec 28, 2017)  
How logx x=1?

Saim said: (Sep 10, 2018)  
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.

Biswa said: (Dec 23, 2019)  
I want to all formula & explanation about logarithms?

Devota said: (Jun 8, 2020)  
I'm not getting this, please anyone explain in detail.

Victor said: (Jun 25, 2020)  
@Saim.

We can't replace it with log2^2 because log2^2 =2log2 not 1.

Chi said: (Jul 3, 2020)  
One of the laws of the log is log10 10=1
log2 2=1
log5 5=1
logx x=1

@Saim.

Log 2 to the power 2 (written as log 2^2) = 2*Log2 and not 1.

Vijju said: (Dec 17, 2020)  
@Chi.

How log 10 10 = 1?

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.