SHL.
Choose the correct option.
If log(2.3) = 0.3617, then log(23) + log(0.23) + log(0.023) =
Answers
Given that:
- log(2.3) = 0.3617
To Find:
- log(23) + log(0.23) + log(0.023) = ?
We know that:
- log(10) = 1
Finding the value of,
log(23) = log{(23/10) × 10}
log(23) = log(2.3) + log(10)
log(23) = 0.3617 + 1
log(23) = 1.3617
log(0.23) = log(2.3/10)
log(0.23) = log(2.3) - log(10)
log(0.23) = 0.3617 - 1
log(0.23) = - 0.6383
log(0.023) = log(2.3/100)
log(0.023) = log(2.3) - log(100)
log(0.023) = log(2.3) - log(10²)
log(0.023) = log(2.3) - 2log(10)
log(0.023) = 0.3617 - 2(1)
log(0.023) = 0.3617 - 2
log(0.023) = - 1.6383
Now we have:
- log(23) = 1.3617
- log(0.23) = - 0.6383
- log(0.023) = - 1.6383
Finding,
log(23) + log(0.23) + log(0.023)
= 1.3617 + (- 0.6383) + (- 1.6383)
= 1.3617 - 0.6383 - 1.6383
= - 0.9149
Hence,
- log(23) + log(0.23) + log(0.023) = - 0.9149
Given that:
log(2.3) = 0.3617
To Find:
log(23) + log(0.23) + log(0.023) = ?
We know that:
log(10) = 1
Finding the value of,
log(23) = log{(23/10) × 10}
log(23) = log(2.3) + log(10)
log(23) = 0.3617 + 1
log(23) = 1.3617
log(0.23) = log(2.3/10)
log(0.23) = log(2.3) - log(10)
log(0.23) = 0.3617 - 1
log(0.23) = - 0.6383
log(0.023) = log(2.3/100)
log(0.023) = log(2.3) - log(100)
log(0.023) = log(2.3) - log(10²)
log(0.023) = log(2.3) - 2log(10)
log(0.023) = 0.3617 - 2(1)
log(0.023) = 0.3617 - 2
log(0.023) = - 1.6383
Now we have:
log(23) = 1.3617
log(0.23) = - 0.6383
log(0.023) = - 1.6383
Finding,
log(23) + log(0.23) + log(0.023)
= 1.3617 + (- 0.6383) + (- 1.6383)
= 1.3617 - 0.6383 - 1.6383
= - 0.9149
Hence,
log(23) + log(0.23) + log(0.023) = - 0.9149