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:
1
3
5
10
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.

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.

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.

Chi said:   4 years ago
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.

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.

Mahesh said:   8 years ago
Anyone please explain that step:2 log10 5 + log10 (5x+1) = log10 (x+5) + log10 10.
How is come?

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.

Victor said:   4 years ago
@Saim.

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

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.

Gilbert Langat said:   2 years ago
@All.

According to me;
Log 5(4t+7) - log5t = 2.


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