Question

If log 8 = 0.9030, express the following:

log 2000

Answer 1

We are given:

log 8 = 0.9030

We need to find:

log 2000

Step 1: Express 2000 in terms of 8 and powers of 10

2000 = 8 × 250

= 8 × (25 × 10)

= 8 × 25 × 10

So:

log 2000 = log (8 · 25 · 10)

= log 8 + log 25 + log 10

Step 2: Substitute known values

• log 8 = 0.9030
• log 25 = log (5²) = 2 log 5 ≈ 2 × 0.6990 = 1.3980
• log 10 = 1

Now add:

log 2000 = 0.9030 + 1.3980 + 1 = 3.3010