Question

(05.01) 4^x = 8^x − 1 a. x=3/4 b. x=1 c. x=3 d. x=6 Algebra 2

Answer 1

Answer:

c. x=3

Step-by-step explanation:

4^x = 8^(x − 1)

4 = 2^2

8 = 2^3

2^2^x = 2^3^(x-1)

We know that a^b^c = a^(b*c)

2^(2x) = 2^(3*(x-1))

2^(2x) = 2^(3x-3)

The bases are the same so the exponents are the same

2x = 3x-3

Subtract 3x from each side

2x-3x = 3x-3-3x

-x = -3

x =3

Answer 2

Answer:

c. x = 3

Step-by-step explanation:

4^x = 8^(x-1)

2²^x = 2³^(x-1)

2^(2x) = 2^(3x-3)

2x = 3x - 3

x = 3