4^x-1×(0.5)^3-2x =(1/8)^x Solve for x
Answers
Answer:
The solution of the expression is x=\frac{5}{7}x=
7
5
Step-by-step explanation:
Given : Expression 4^{x-1}\times (0.5)^{3-2x}=(\frac{1}{8})^x4
x−1
×(0.5)
3−2x
=(
8
1
)
x
To find : Solve the expression ?
Solution :
4^{x-1}\times (0.5)^{3-2x}=(\frac{1}{8})^x4
x−1
×(0.5)
3−2x
=(
8
1
)
x
We solve the expression,
(2^2)^{x-1}\times (\frac{1}{2})^{3-2x}=(\frac{1}{2^3})^x(2
2
)
x−1
×(
2
1
)
3−2x
=(
2
3
1
)
x
(2)^{2x-2}\times (2^{-1})^{3-2x}=2^{-3x}(2)
2x−2
×(2
−1
)
3−2x
=2
−3x
(2)^{2x-2}\times 2^{2x-3}=2^{-3x}(2)
2x−2
×2
2x−3
=2
−3x
(2)^{2x-2+2x-3}=2^{-3x}(2)
2x−2+2x−3
=2
−3x
(2)^{4x-5}=2^{-3x}(2)
4x−5
=2
−3x
(2)^{4x}\times 2^{-5}=2^{-3x}(2)
4x
×2
−5
=2
−3x
\frac{(2)^{4x}}{2^{5}}=2^{-3x}
2
5
(2)
4x
=2
−3x
\frac{(2)^{4x}}{2^{-3x}}=2^{5}
2
−3x
(2)
4x
=2
5
(2)^{4x+3x}=2^{5}(2)
4x+3x
=2
5
(2)^{7x}=2^{5}(2)
7x
=2
5
On comparing the powers as base are same,
7x=57x=5
x=\frac{5}{7}x=
7
5
Therefore, The solution of the expression is x=\frac{5}{7}x=
7
5
Step-by-step explanation:
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