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

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

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4^x=5*2^x-4

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

x = 2, x = 0

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

u^{2} = 5 u - 4 : 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

8^{x} - 2^{2 - 3 x} = 3

5^{x + 2} = 625

2 (3^{x - 3}) = 79

4 e^{x} = 16

2^{4 x} = 78