solve 2^x+2 - 6^x - 2×3^2x+2 = 0
Answers
Answer:
We have,
2
2x+2
−6
x
−2.3
2x+2
=0
now,
⇒2
2(x+1)
−6
x
−2.3
2(x+1)
=0
⇒4
(x+1)
−6
x
−2.9
(x+1)
=0
⇒4
x
.4−2
x
.3
x
−2.(9
x
.9)=0
⇒4.(2
x
)
2
−2
x
.3
x
−18(3
x
2
)=0
on divide (2
x
2
) and we get,
⇒
(2
x
)
2
4.(2
x
)
2
−
(2
x
)
2
2
x
.3
x
−18[(
2
3
)
x
]
2
=0
⇒4−(
2
3
)
x
−18[(
2
3
)
x
]
2
=0
let, (
2
3
)
x
=y−−−−(1)
now,
⇒4−y−18y
2
=0
on factorize
⇒4−(9−8)y−18y
2
=0
⇒4−9y+8y−18y
2
=0
⇒1(4−9y)+2y(4−9y)=0
⇒(4−9y)(1+2y)=0
⇒4−9y=0,1+2y=0
⇒y=
9
4
→ (choose), y=
2
−1
(not choose)
using equation (1)
(
2
3
)
x
=
9
4
⇒(
2
3
)
x
=(
3
2
)
2
on reciprocal
⇒(
2
3
)
x
=(
2
3
)
−2
then, comparing,
x=−2
Hence, this is the answer.
Step-by-step explanation: