Starting equation
:
(
4
9
)
x+1
=
(
27
8
)
x + 6
Re-write
(
4
9
)
=
(
2
3
)
2
and
(
27
8
)
=
(
2
3
)
-
3
The above two revisions result in this equation
:
[(
2
3
)
2
]
x+1
=
[(
2
3
)
-
3
]
x + 6
and using
Rules for exponents
:
(
2
3
)
2(x+1)
=
(
2
3
)
-
3(x + 6)
If the powers are equal, and the bases (here, 3) are equal then the exponents must also be equal
:
2(x + 1) =
-
3(x + 6)
2x+2 =
-
3x
-
18
5x =
-
20
x = -4