Answer:
x
=
7
9
.
Step-by-step explanation:
x
=
7
9
.
Step-by-step explanation:
Remember the rules of logarithms:
log
a
−
log
b
=
log
(
a
b
)
. Using this, we get
log
x
−
log
(
x
+
7
)
=
−
1
⇒
log
(
x
x
+
7
)
=
−
1
Now we remember that
log
c
=
d
⇔
c
=
10
d
. Essentially what we're doing there is taking 10 to the power of both sides, and since
10
x
and
log
x
are inverse functions, they cancel off.
f
−
1
[
f
(
x
)
]
=
x
. So we get
log
(
x
x
+
7
)
=
−
1
(
⇒
10
log
(
x
x
+
7
)
=
10
−
1
)
⇒
x
x
+
7
=
10
−
1
⇒
x
=
x
+
7
10
⇒
10
x
=
x
+
7
⇒
9
x
=
7
⇒
x
=
7
9
So
x
=
7
/
9
is our answer.