Question

If log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, find the value of `log 1 1/6`.

Answer 1

Given:

log 2 = 0.3010

log 3 = 0.4771

log 7 = 0.8451

To find:

`log(1 1/6)` = ?

Calculation:

Step 1: Convert to an improper fraction:

`1 1/6 = 7/6`

so,

`log (1 1/6) = log (7/6)`

Step 2: Apply the logarithm quotient rule:

`log (a/b) = log a - log b`

`log(7/6) = log 7 - log 6`

Step 3: Express log 6:

log 6 = log (2 × 3)

= log 2 + log 3

Now substitute log 2 = 0.3010 and log 3 = 0.4771 into the expression.

log 6 = 0.3010 + 0.4771

= 0.7781

Step 4: Substitute values:

`log(7/6)` = log 7 − log 6`

= 0.8451 − 0.7781

= 0.0670