What is the answer to 5^{2t+1}-26*5^t+5=0 ?

The answer to 5^{2t+1}-26*5^t+5=0 is t=1,t=-1

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5^{2t+1}-26*5^t+5=0

5^{2 t + 1} - 26 \cdot 5^{t} + 5 = 0

t = 1, t = - 1

Solution steps

5^{2 t + 1} - 26 \cdot 5^{t} + 5 = 0

Apply exponent rules

(5^{t})^{2} \cdot 5^{1} - 26 \cdot 5^{t} + 5 = 0

Rewrite the equation with

5^{t} = u

(u)^{2} \cdot 5^{1} - 26 u + 5 = 0

Solve

u^{2} \cdot 5^{1} - 26 u + 5 = 0 : u = 5, u = \frac{1}{5}

u = 5, u = \frac{1}{5}

Substitute back

u = 5^{t},

solve for

t

Solve

5^{t} = 5 : t = 1

Solve

5^{t} = \frac{1}{5} : t = - 1

t = 1, t = - 1

2^{x^{2} - x + 3} = 32

3^{2 x + 5} = 7^{x}

e^{4 x} = \frac{1}{64}

7^{- 3 x} = 1 1^{x + 8}

What is the answer to 5^{2t+1}-26*5^t+5=0 ?
The answer to 5^{2t+1}-26*5^t+5=0 is t=1,t=-1
Solve for t: 5^{2t+1}-26*5^t+5=0
The solution is t=1,t=-1