What is the answer to 4^x=4+3\times 2^x ?

The answer to 4^x=4+3\times 2^x is x=2

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4^x=4+3\times 2^x

4^{x} = 4 + 3 \cdot 2^{x}

x = 2

Solution steps

4^{x} = 4 + 3 \cdot 2^{x}

Apply exponent rules

(2^{x})^{2} = 4 + 3 \cdot 2^{x}

Rewrite the equation with

2^{x} = u

(u)^{2} = 4 + 3 u

Solve

u^{2} = 4 + 3 u : 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 :

No Solution for

x \in R

x = 2

1 6^{x - 1} = 102 4^{x - 1}

- 3 e^{- 3 x} - 4 e^{- 2 x} + 5 e^{- x} + 2 = 0

8 1^{x + 2} = 2 7^{5 x + 4}

4^{x - 15} = \frac{1}{2}

x, 2^{x} = 16

What is the answer to 4^x=4+3\times 2^x ?
The answer to 4^x=4+3\times 2^x is x=2
Solve for x: 4^x=4+3\times 2^x
The solution is x=2