Question

Given log 2 = a, log 3 = b, express in terms of a and b.

log 125

Answer 1

Given: log 2 = a, log 3 = b

To Find: log 125

Calculation:

Step 1: Express 125 as a power of 5:

125 = 5³

Thus:

log 125 = log (5³) = 3 log 5

Step 2: Express log 5 in terms of a and b:

We know that:

log 10 = 1 and log 10 = log (2 × 5)

Using the property log (ab) = log a + log b, we get:

1 = log 2 + log 5

Since log 2 = a, we have:

1 = a + log 5

So:

log 5 = 1 – a

Step 3: Substitute and simplify:

Now substitute log 5 = 1 – a into the equation for log 125:

log 125 = 3 log 5

log 125 = 3 (1 – a)

log 125 = 3 – 3a