Question

If log 8 = 0.9030, express the following:

`log  5/4`

Answer 1

Given: log 8 = 0.9030

To Find: `log (5/4)`

Calculation:

Step 1: We know that

`log  a/b` = log a − log b

So, `log  5/4 = log 5 - log 4`

Step 2: We can express 8 in terms of 2:

⇒ 8 = 2³

⇒ log 8 = log (2³)

⇒ 3 log 2

Hence, 3 log 2 = 0.9030

log 2 = `0.9030/3`

log 2 = 0.3010

Step 3: Now, log 4 = log (2²)

2 log 2 = 2 × 0.3010

= 0.6020

and log 5 = 1 − log 2

= 1 − 0.3010

= 0.6990

Step 4: Substitute in `log ⁡ 5/4` = log ⁡5 − log ⁡4:

`log (5/4)` = 0.6990 − 0.6020

`log (5/4)` = 0.0970