What is the answer to 4^x+2^{x+3}=48 ?

The answer to 4^x+2^{x+3}=48 is x=2

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4^x+2^{x+3}=48

4^{x} + 2^{x + 3} = 48

x = 2

Solution steps

4^{x} + 2^{x + 3} = 48

Apply exponent rules

(2^{x})^{2} + 2^{x} \cdot 2^{3} = 48

Rewrite the equation with

2^{x} = u

(u)^{2} + u \cdot 2^{3} = 48

Solve

u^{2} + u \cdot 2^{3} = 48 : u = 4, u = - 12

u = 4, u = - 12

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = - 12 :

No Solution for

x \in R

x = 2

x, e^{x} + 5 e^{- x} = 6

n, 2^{n} = 1000000

3 \cdot 3^{\frac{x}{5}} = 1

2^{3 x} = 128

(25)^{4 x^{2} - 3 x} = \frac{1}{5}