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

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.