Question

If log 2 = x and log 3 = y, express the following in terms of x and y.

log 250

Answer 1

Given: log 2 = x, log 3 = y (logs are base 10, so log 10 = 1).

Step-wise calculation:

1. 250 = 2 × 5³

2. log 250 = log 2 + log (5³)

= log 2 + 3 log 5

3. `log 5 = log (10/2)`

= log 10 – log 2

= 1 – x

4. Substitute:

log 250 = x + 3(1 – x)

= x + 3 – 3x

= 3 – 2x