# Aptitude - Logarithm - Discussion

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

9.

If log

_{10}5 + log_{10}(5*x*+ 1) = log_{10}(*x*+ 5) + 1, then*x*is equal to:Answer: Option

Explanation:

log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + 1

log_{10} 5 + log_{10} (5*x* + 1) = log_{10} (*x* + 5) + log_{10} 10

log_{10} [5 (5*x* + 1)] = log_{10} [10(*x* + 5)]

5(5*x* + 1) = 10(*x* + 5)

5*x* + 1 = 2*x* + 10

3*x* = 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.

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.

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.

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.

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?

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.

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.

According to me;

Log 5(4t+7) - log5t = 2.

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