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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