log (X2+1) (2x+x) <1 [x+2 > 0]
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Answer:
Explanation:
1
. Use the log property,
log
b
(
m
n
)
=
log
b
(
m
)
−
log
b
(
n
)
to simplify the left side of the equation.
log
(
2
x
+
1
)
−
log
(
x
−
2
)
=
1
log
(
2
x
+
1
x
−
2
)
=
1
2
. Use the log property,
log
b
(
b
x
)
=
x
, to rewrite the right side of the equation.
log
(
2
x
+
1
x
−
2
)
=
log
(
10
)
3
. Since the equation now follows a "
log
=
log
" situation, where the bases are the same on both sides of the equation, rewrite the equation without the "log" portion.
2
x
+
1
x
−
2
=
10
4
. Solve for
x
.
2
x
+
1
=
10
(
x
−
2
)
2
x
+
1
=
10
x
−
20
8
x
=
21
∣
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
x
=
21
8
a
a
∣
∣
∣
−−−−−−−−−−−
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