Question

If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.

Answer 1

Given that
m = log 20 and n = log 25
We also have
2log( x - 4 ) = 2m - n
⇒ 2log ( x - 4 ) = 2log 20 - log 25
⇒  log( x - 4 )² = log20² - log 25
⇒  log( x - 4 )² = log 400 - log 25
⇒  log( x - 4 )² = log `400/25`
⇒  ( x - 4 )² = `400/25`
⇒  ( x - 4 )² = 16
⇒ x - 4 = 4
⇒ x = 4 + 4
⇒ x = 8.