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

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**

**Solve the equation t^4+10t-11=0**

It is not possible to solve the equation you have given t^4 + 10t - 11 = 0.

Instead, here is the solution for t^4 + 10 t^2 - 11 = 0

let t^2 = x

=> x^2 + 10x - 11 = 0

=> x^2 + 11x - x - 11 = 0

=> x(x + 11) - 1(x + 11) = 0

=> (x - 1)(x + 11) = 0

=> x = 1 and x = -11

t^2 = 1

=> t1 = 1

=> t2 = -1

t^2 = -11

=> t3 = i*sqrt 11

=> t4 = -i*sqrt 11

**The solutions of the equation t^4 + 10 t^2 - 11 = 0 are {-1 , 1,
i*sqrt 11, -i*sqrt 11}**

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