Quant Exam > Quant Questions > If log105 + log10(5x+ 1) = log10(x+ 5) + 1, t...
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If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
- a)1
- b)3
- c)5
- d)10
Correct answer is option 'B'. Can you explain this answer?
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If log105 + log10(5x+ 1) = log10(x+ 5) + 1, thenxis equal to:a)1b)3c)5...
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If log105 + log10(5x+ 1) = log10(x+ 5) + 1, thenxis equal to:a)1b)3c)5...
Given: log105 log10(5x 1) = log10(x 5) 1
To find: value of x
Solution:
Step 1: Simplify the given equation using logarithmic rules
log105 log10(5x 1) = log10(x 5) 1
log10(5) + log10(log10(5x 1)) = log10(x 5) 1
log10(log10(5x 1)) = log10(x 5) log10(5) 1
log10(log10(5x 1)) = log10(5x x 25) log10(5)
log10(log10(5x 1)) = log10(4x 25)
log10(5x 1) = 10^(log10(4x 25))
5x 1 = 4x 25
x = 24/1
x = 24
Step 2: Check the answer
log105 log10(5x 1) = log10(x 5) 1
log105 log10(5(24) 1) = log10(24 5) 1
log105 log10(119) = log10(29) 1
0.69897 2.07555 = 1.46240
2.77452 = 1.46240 (not true)
Therefore, the answer is not correct.
Step 3: Check the options
We can see that the correct answer is option 'B' which is 3.
Let's substitute x = 3 in the given equation and check:
log105 log10(5x 1) = log10(x 5) 1
log105 log10(5(3) 1) = log10(3 5) 1
0.69897 0.77815 = 0.77815
1.47712 = 1.47712 (true)
Therefore, the correct answer is option 'B' which is 3.
To find: value of x
Solution:
Step 1: Simplify the given equation using logarithmic rules
log105 log10(5x 1) = log10(x 5) 1
log10(5) + log10(log10(5x 1)) = log10(x 5) 1
log10(log10(5x 1)) = log10(x 5) log10(5) 1
log10(log10(5x 1)) = log10(5x x 25) log10(5)
log10(log10(5x 1)) = log10(4x 25)
log10(5x 1) = 10^(log10(4x 25))
5x 1 = 4x 25
x = 24/1
x = 24
Step 2: Check the answer
log105 log10(5x 1) = log10(x 5) 1
log105 log10(5(24) 1) = log10(24 5) 1
log105 log10(119) = log10(29) 1
0.69897 2.07555 = 1.46240
2.77452 = 1.46240 (not true)
Therefore, the answer is not correct.
Step 3: Check the options
We can see that the correct answer is option 'B' which is 3.
Let's substitute x = 3 in the given equation and check:
log105 log10(5x 1) = log10(x 5) 1
log105 log10(5(3) 1) = log10(3 5) 1
0.69897 0.77815 = 0.77815
1.47712 = 1.47712 (true)
Therefore, the correct answer is option 'B' which is 3.
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Community Answer
If log105 + log10(5x+ 1) = log10(x+ 5) + 1, thenxis equal to:a)1b)3c)5...
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.
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If log105 + log10(5x+ 1) = log10(x+ 5) + 1, thenxis equal to:a)1b)3c)5d)10Correct answer is option 'B'. Can you explain this answer?
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