What is the answer to 4^x-6(2^x)-16=0 ?

The answer to 4^x-6(2^x)-16=0 is x=3

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4^x-6(2^x)-16=0

4^{x} - 6 (2^{x}) - 16 = 0

x = 3

Solution steps

4^{x} - 6 (2^{x}) - 16 = 0

Apply exponent rules

(2^{x})^{2} - 6 \cdot 2^{x} - 16 = 0

Rewrite the equation with

2^{x} = u

(u)^{2} - 6 u - 16 = 0

Solve

u^{2} - 6 u - 16 = 0 : u = 8, u = - 2

u = 8, u = - 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = - 2 :

No Solution for

x \in R

x = 3

a, x^{a + b} = x^{a} + x^{b}

4 (4^{2 x}) - 17 (4^{x}) + 4 = 0

2^{2 x + 3} - 8 \cdot 2^{x + 1} + 8 = 0

2^{2 x - 5} = 8

7^{10} = 7^{5} \cdot 7^{f}