What is the answer to 4^x-6(2^x)=-8 ?

The answer to 4^x-6(2^x)=-8 is x=2,x=1

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4^x-6(2^x)=-8

4^{x} - 6 (2^{x}) = - 8

x = 2, x = 1

Solution steps

4^{x} - 6 (2^{x}) = - 8

Apply exponent rules

(2^{x})^{2} - 6 \cdot 2^{x} = - 8

Rewrite the equation with

2^{x} = u

(u)^{2} - 6 u = - 8

Solve

u^{2} - 6 u = - 8 : u = 4, u = 2

u = 4, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = 2 : x = 1

x = 2, x = 1

5^{2 x + 1} = \frac{1}{625}

(\frac{1}{9})^{x} = 27

- 6 = - 7 + 5 e^{- 7 x}

5 (2^{2 x}) - 15 (2^{x + 1}) + 40 = 0

2^{x^{2}} = 1 6^{x - 1}