How to find the real x in equation log4 (x+4)+log4 1/(x+1) -1=0?

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We have to solve : log(4) (x+4) + log(4) 1/(x+1) - 1 = 0

Use the relation log a + log b = log (a*b)

log(4) (x+4) + log(4) 1/(x+1) - 1 = 0

=> log(4) (x + 4) / (x + 1)  - 1 = 0

=> log(4) (x + 4) / (x + 1)  = 1

=> (x + 4) / (x + 1) = 4

=> x + 4 = 4(x + 1)

=> x + 4 = 4x + 4

=> 3x = 0

=> x = 0

Log 4 and log 1 exist, so x = 0 is a valid solution.

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