# 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

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?