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.
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