Question

(4)
Solve : log x + log (x + 1) = 2

Answer 1

Hey Buddy

Here's The Answer

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Properties Used :

1. => log a + log b = log ( a×b )

2. => log 10 = 1

3. => a log b = log bᵃ

Given :

log x + log( x + 1 ) = 2

By using property 1.

=> log ( x [ x + 1 ] ) = 2

=> log( x² + x ) = 2

We can also write it as :

=> log( x² + x ) = 2 × 1

We can replace 1 by log 10

=> log( x² + x ) = 2 log 10

By property 3.

=> log( x² + x ) = log 10²

Cancelling log from both side

=> x² + x = 10²

=> x² + x - 100 = 0

Hope It Helps.