What is the answer to 25^x+1=26(5^{x-1}) ?

The answer to 25^x+1=26(5^{x-1}) is x=1,x=-1

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25^x+1=26(5^{x-1})

2 5^{x} + 1 = 26 (5^{x - 1})

x = 1, x = - 1

Solution steps

2 5^{x} + 1 = 26 (5^{x - 1})

Apply exponent rules

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

Rewrite the equation with

5^{x} = u

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

Solve

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

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

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

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

x = 1, x = - 1

5^{x} - 5^{(5 - x)} = 150

4^{x} = 89

2^{x + 3} - 2^{x} = k (x) (2^{x})

2^{5 x - 1} = 3^{2 x}

1 0^{x} = 10000

What is the answer to 25^x+1=26(5^{x-1}) ?
The answer to 25^x+1=26(5^{x-1}) is x=1,x=-1
Solve for x: 25^x+1=26(5^{x-1})
The solution is x=1,x=-1