log(4x -3) - log (x+4)= log(2) find the value of x?
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Answer:
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Answered by
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Step-by-step explanation:
In this type of equations, our goal is to arrive to an expresion like
log
b
A
=
log
b
C
from this, we conclude
A
=
C
Lets see
log
4
x
=
2
−
log
4
(
x
+
6
)
We know that
2
=
log
4
16
. then
log
4
x
=
log
4
16
−
log
4
(
x
+
6
)
=
log
4
(
16
x
+
6
)
applying the rule
log
(
A
B
)
=
log
A
−
log
B
So, we have
x
=
16
x
+
6
x
2
+
6
x
−
16
=
0
by quadratic formula
x
=
−
6
±
√
36
+
64
2
=
−
6
±
10
2
Solutions are
x
1
=
−
8
and
x
2
=
2
we reject negative and the only valid solution is
x
2
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