What is the answer to 4^x-5*2^x+4=0 ?

The answer to 4^x-5*2^x+4=0 is x=2,x=0

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4^x-5*2^x+4=0

4^{x} - 5 \cdot 2^{x} + 4 = 0

x = 2, x = 0

Solution steps

4^{x} - 5 \cdot 2^{x} + 4 = 0

Apply exponent rules

(2^{x})^{2} - 5 \cdot 2^{x} + 4 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 5 u + 4 = 0

Solve

u^{2} - 5 u + 4 = 0 : u = 4, u = 1

u = 4, u = 1

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 1 : x = 0

x = 2, x = 0

3 e^{x} = 10

\frac{( ( 3 ^{x} ) ^{3 x + 1} )}{( 2 7 ^{2 x} )} = 9^{5 x - 1}

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

2^{x + 1} + 4^{x} = 80

7^{3 p - 5} = \frac{1}{( 4 9 ^{p} )}