Question

Use the approximate logarithm values below to estimate the value of each of the following logarithms. Indicate which properties you used.

log(12)

Answer 1

log(12) = 1.0791

Explanation:

To solve:

log(12)

Now,

log(12) can also be written as :

⇒ log(4 × 3)

or

⇒ log(2 × 2 × 3)

or

⇒ log(2² × 3)

also,

we know the property of log function that

1) log(A × B) = log(A) + log(B)

2) log(Aᵇ) = b × log(A)

Thus applying the property (1) on the on the above rewritten form, we get

⇒ log(2² × 3) = log(2²) + log(3)

now applying the property 2, we get

⇒ 2 × log(2) + log(3)

also,

log(2) = 0.3010

log(3) = 0.4771

substituting the above values, we get

⇒ 2 × 0.3010 + 0.4771

or

⇒ 0.6020 + 0.4771

or

⇒ 1.0791

Hence,

log(12) = 1.0791