(x3_2x-2x+5)
loga = logh
Answers
Step-by-step explanation:
Given:
log
(
x
−
3
)
+
log
(
x
−
5
)
=
log
(
2
x
−
9
)
Step 1: Rewrite the expression using sum to product rule
log
[
(
x
−
3
)
(
x
−
5
)
]
=
log
(
2
x
−
9
)
log
(
x
2
−
3
x
−
5
x
+
15
)
=
log
(
2
x
−
9
)
Step 2 : Rewrite in exponential form with base to ("drop" log since we have sam log both side of equation)
10
log
(
x
2
−
8
x
+
15
)
=
10
log
(
2
x
−
9
)
x
2
−
8
x
+
15
=
2
x
−
9
Step 3: Manipulate equation to write it in quadratic form
a
x
2
+
b
x
+
c
=
0
x
2
−
8
x
+
15
=
2
x
−
9
x
2
−
10
x
+
24
=
0
Step 4: This can be solve by factoring
Step 5: Check solution- can't have negative number as argument for the logarithm
Check
x
=
−
2
log
(
−
2
−
3
)
+
log
(
−
2
−
5
)
=
log
(
2
⋅
−
2
−
9
)
log
(
−
5
)
+
log
(
−
7
)
=
log
(
−
13
)
Can't have negative as argument for logarithm, therefore
x
=
−
2
is extraneous solution
** 2 number multiply equal to 24
like
−
12
⋅
2
or
−
6
⋅
−
4
or
−
8
⋅
3
or
−
2
⋅
12
e
t
c
.
**Add equal to
−
10
−
12
+
2
=
−
10