Answer:
x=10
3
−5,y=
10
3
−5
4
�
=
1
0
−
3
−
5
,
�
=
−
2
1
0
−
3
−
5
x=10
−
3
−5,y=
10
−
3
−5
−2
Step-by-step explanation:
log
2
(a+5)=3
Since
log
2
(
�
)
=
3
log
2
(x)=3 implies
log
(
�
)
=
3
log(x)=
3
or
log
(
�
)
=
−
3
log(x)=−
3
, we'll solve each equation separately:
log
(
�
+
5
)
=
3
log(a+5)=
3
�
+
5
=
1
0
3
a+5=10
3
�
=
1
0
3
−
5
a=10
3
−5
log
(
�
+
5
)
=
−
3
log(a+5)=−
3
�
+
5
=
1
0
−
3
a+5=10
−
3
�
=
1
0
−
3
−
5
a=10
−
3
−5
Therefore, the solutions for
�
a are
�
=
1
0
3
−
5
a=10
3
−5 and
�
=
1
0
−
3
−
5
a=10
−
3
−5.
Now, we can find the corresponding values of
�
b using the values of
�
�
ab obtained earlier:
For
�
�
=
4
ab=4, we substitute
�
=
1
0
3
−
5
a=10
3
−5 and solve for
�
b:
�
=
�
�
�
=
4
1
0
3
−
5
b=
a
ab
=
10
3
−5
4
For
�
�
=
−
2
ab=−2, we substitute
�
=
1
0
−
3
−
5
a=10
−
3
−5 and solve for
�
b:
�
=
�
�
�
=
−
2
1
0
−
3
−
5
b=
a
ab
=
10
−
3
−5
−2
Therefore, the solutions for
�
x and
�
y simultaneously are:
�
=
1
0
3
−
5
,
�
=
4
1
0
3
−
5
x=10
3
−5,y=
10
3
−5
4
�
=
1
0
−
3
−
5
,
�
=
−
2
1
0
−
3
−
5
x=10
−
3
−5,y=
10
−
3
−5
−2
