What is the answer to (2+sqrt(3))^x+(2-sqrt(3))^x=4 ?

The answer to (2+sqrt(3))^x+(2-sqrt(3))^x=4 is x=1,x=-1

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(2+sqrt(3))^x+(2-sqrt(3))^x=4

(2 + 3)^{x} + (2 - 3)^{x} = 4

x = 1, x = - 1

Solution steps

(2 + 3)^{x} + (2 - 3)^{x} = 4

Apply exponent rules

(2 + 3)^{x} + ((2 + 3)^{x})^{- 1} = 4

Rewrite the equation with

(2 + 3)^{x} = u

u + (u)^{- 1} = 4

Solve

u + u^{- 1} = 4 : u = 2 + 3, u = 2 - 3

u = 2 + 3, u = 2 - 3

Substitute back

u = (2 + 3)^{x},

solve for

x

Solve

(2 + 3)^{x} = 2 + 3 : x = 1

Solve

(2 + 3)^{x} = 2 - 3 : x = - 1

x = 1, x = - 1

e^{x} - e^{- x} = - 1

1 6^{8^{- 2 7^{- x}}} = 4

4^{4 x + 1} = 16

4^{x - 5} = 8^{2 x - 2}

\frac{2 ^{8 - x}}{3 2 ^{x + 12}} = 2^{3 x - 7}

What is the answer to (2+sqrt(3))^x+(2-sqrt(3))^x=4 ?
The answer to (2+sqrt(3))^x+(2-sqrt(3))^x=4 is x=1,x=-1
Solve for x: (2+sqrt(3))^x+(2-sqrt(3))^x=4
The solution is x=1,x=-1