Question

Express as a single logarithm:

1 + log 4 – log 5

Answer 1

1 + log 4 – log 5

We know that

1 = log 10  ...(since log ⁡10 = 1 when the base is 10.)

∴ log 10 + log 4 – log 5

Using the rules log ⁡a − log ⁡b = `log⁡(a/b)` and log⁡ a + log ⁡b = log ⁡(ab),

= log (10 × 4) – log 5

= log 40 – log 5

= `log (40/5)`

= log 8