Question

If log 9 = 0.9542, find the value of log 30.

Answer 1

log 9 = 0.9542

We need to find the value of log 30.

Step 1: Express 30 as a product:

30 = 3 × 10

Step 2: Use the logarithmic property:

log (ab) = log a + log b

log 30

= log(3 × 10)

= log 3 + log 10

Since log 10 = 1, we now need to find log 3.

Step 3: Relate log 3 to log 9:

We know that:

log 9

= log(3²)

= 2 log 3

Given that log 9 = 0.9542, we can find log 3:

2 log 3 = 0.9542

⇒ `log 3 = 0.9542/2`

⇒ log 3 = 0.4771

Step 4: Calculate log 30:

Now, substitute log 3 = 0.4771 and log 10 = 1 into the equation for log 30:

log 3 = 0.4771 + 1

log 3 = 1.4771