Question

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 0.24

Answer 1

We are given:

• log 2 = a
• log 3 = b

We are to express:

log 0.24

Step 1: Express 0.24 as a fraction of primes

`0.24 = 24/100`

= `(2^3 * 3)/(2^2 * 5^2)`

= `(2 * 3)/5^2`

= `6/25`

So:

`log 0.24 = log (6/25) = log 6 - log 25`

Now express each term:

log 6 = log (2 · 3) = log 2 + log 3 = a + b

log 25 = log (5²) = 2 log 5

Final Expression:

log 0.24 = a + b – 2 log 5