Question

If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.

Answer 1

x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108
⇒ x = log 108 - log 4 - 2 log 5 - 3 log 3 - 2 log 2
= log (2² . 3³) - log 2² - log 5² - log 3³ - log 2²
= `"log"((2^2. 3^3)/(2^2 . 5^2 . 3^3. 2^2))`

= `"log"(1/100)`
⇒ x
= log 1 - log 100
= 0 - 2
= -2
∴ x = -2.