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