Question

If p = log 20 and q = log 25 , find the value of x , if 2log( x + 1 ) = 2p - q. 

Answer 1

Given that
p = log 20 and q = log 25
We also have
2 log( x + 1 ) = 2p - q
⇒ 2log( x + 1 ) = 2 log 20 - log 25
⇒ log( x + 1 )² = log20² - log 25
⇒  log( x + 1 )² = log 400 - log 25
⇒ log( x + 1 )² = log`400/25`
⇒ log( x + 1 )² = log 16
⇒ log( x + 1 )² = log 4² 
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3.