Question

Given log 9 = a, express log 300 and `log sqrt(0.009)` in terms of a.

Answer 1

Given, log 9 = a

We know that 9 = 3², so

log3² = a

2 log ⁡3 = a

log 3 = `a/2`​

(i) To find log ⁡300:

log 300 = log (3 × 100)

= log 3 + log 100

= `a/2 + 2`  ...(since log 100 = 2)

Hence, log 300 = `a/2 + 2`

(ii) To find `bb(log sqrt(0.009))`:

`log sqrt(0.009) = 1/2 log 0.009`

= `1/2 log (9/1000)`

= `1/2 (log 9 - log 1000)`

= `1/2 (a - 3)`

Hence, `log sqrt(0.009) = 1/2 (a - 3)`