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

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

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5^{1+x}+5^{1-x}=26

5^{1 + x} + 5^{1 - x} = 26

x = 1, x = - 1

Solution steps

5^{1 + x} + 5^{1 - x} = 26

Apply exponent rules

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

Rewrite the equation with

5^{x} = u

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

Solve

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

2^{x + 3} = 512

9^{x - 1} = 4

2^{3 x - 1} = 4^{x}

3^{x} + 3^{x - 1} - 3^{x - 2} = 11

1 6^{2 x - 3} = 8

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