# solve these questions: 8^x-1 = 4, x^/2 = 2 1/4 and (1/2)^x = (1/64)^2x+3as well as: 8^x-1 = 4 x^/2 = 2 1/4 (1/2)^x = (1/64)^2x+3

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To solve the first exponential equation, we'll have to create matching bases, such as;

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

We'll multiply the superscripts:

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

Now, we'll manage the right side and we'll write 4 as a power of 2:

4 = 2^2

We'll re-write the equation:

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

Since the bases are matching, we'll apply one to one rule:

3(x-1) = 2

3x - 3 = 2

3x = 3 + 2

3x = 5

x = 5/3

The solution of the 1st. equation is x = 5/3.

Since the 2nd expression is not so clear, we'll solve the 3rd equation.

We'll manage the right side and we'll re-write 1/64 as a power of 1/2.

1/64 = (1/2)^6

We'll raise both sides to the power (2x+3):

(1/64)^(2x+3) = (1/2)^6(2x+3)

We'll re-write the equation:

(1/2)^x = (1/2)^6(2x+3)

Since the bases are matching, we'll apply one to one rule:

x = 6(2x+3)

x = 12x + 18

11x = -18

x = -18/11

The solution of the 1st equation is x = 5/3 and the solution of the 3rd equation is x = -18/11.