What is the answer to 4^x+2^{x+3}=128 ?

The answer to 4^x+2^{x+3}=128 is x=3

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4^x+2^{x+3}=128

4^{x} + 2^{x + 3} = 128

x = 3

Solution steps

4^{x} + 2^{x + 3} = 128

Apply exponent rules

(2^{x})^{2} + 2^{x} \cdot 2^{3} = 128

Rewrite the equation with

2^{x} = u

(u)^{2} + u \cdot 2^{3} = 128

Solve

u^{2} + u \cdot 2^{3} = 128 : u = 8, u = - 16

u = 8, u = - 16

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = - 16 :

No Solution for

x \in R

x = 3

81 \cdot 9^{- 2 b - 2} = 27

63 = 3 3^{x}

9^{6} = (3^{2})^{2 x - 2}

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

7^{2 x} - 56 \cdot 7^{x} + 343 = 0