What is the real solution of equation 5^(t+1)=4*5^t+1

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We have to solve the equation: 5^(t+1) = 4*5^t + 1

5^(t+1) = 4*5^t + 1

=> 5^t * 5 = 4* 5^t + 1

let y = 5^t

=> y*5 = 4*y + 1

=>5y - 4y = 1

=> y = 1

Now 5^t = y = 1

=> t = 0 , as any number raised to the power 0 is 1.

Therefore, we get the solution t = 0 .

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