What is the answer to 4^x+1=2^{x+1} ?

The answer to 4^x+1=2^{x+1} is x=0

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4^x+1=2^{x+1}

4^{x} + 1 = 2^{x + 1}

x = 0

Solution steps

4^{x} + 1 = 2^{x + 1}

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

u^{2} + 1 = u \cdot 2^{1} : u = 1

u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 1 : x = 0

x = 0

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

2^{x^{2} - 1} = 8

5^{2 x + 1} = 25

1.0 1^{x} = 2