Respuesta:
x=1
Explicación paso a paso:
To solve the equation
8
1
4
−
1
=
9
+
5
81
4x−1
=9
x+5
, you can rewrite both sides with the same base, preferably a base that's a power of 3 or 9 to simplify. Since 81 is
3
4
3
4
and 9 is
3
2
3
2
, let's rewrite them in terms of 3:
8
1
4
−
1
=
(
3
4
)
4
−
1
=
3
4
(
4
−
1
)
=
3
16
−
4
81
4x−1
=(3
4
)
4x−1
=3
4(4x−1)
=3
16x−4
9
+
5
=
(
3
2
)
+
5
=
3
2
(
+
5
)
=
3
2
+
10
9
x+5
=(3
2
)
x+5
=3
2(x+5)
=3
2x+10
Now, the equation becomes:
3
16
−
4
=
3
2
+
10
3
16x−4
=3
2x+10
Since the bases are the same, you can equate the exponents:
16
−
4
=
2
+
10
16x−4=2x+10
Now, solve for
x:
16
−
2
=
10
+
4
16x−2x=10+4
14
=
14
14x=14
=
1
x=1
So,
=
1
x=1 is the solution.