Solve for real t 11^(t+1) -1=4*11^t

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We have to solve 11^(t+1) -1=4*11^t for t.

11^(t+1) -1=4*11^t

=> 11^t*11 - 1 = 4*11^t

let 11^t = x

=> 11x - 1 = 4x

=> 7x = 1

=> x= 1/7

11^t = 1/7

Here the bases are different, so we have to use the log function.

log 11^t = log (1/7)

=> t* log 11 = -log 7

=> t = -log 7 / log 11

The required value of t is -log 7 / log 11

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