solve.
log 10^ x + log 10^ (x-15)=2
Answers
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Step-by-step explanation:
Explanation:
In general:
log
n
(
a
)
+
log
n
(
b
)
=
log
n
(
a
b
)
Therefore:
log
10
(
x
+
21
)
+
log
10
(
x
)
=
log
10
(
x
2
+
21
x
)
By the definition of a logarithm:
log
10
(
x
2
+
21
x
)
=
2
⇒
10
2
=
x
2
+
21
x
By solving this as a quadratic:
100
=
x
2
+
21
x
x
2
+
21
x
−
100
=
0
(
x
−
4
)
(
x
+
25
)
=
0
x
=
4
or
x
=
−
25
(are solutions to the equation), but obviously you can't have a negative within a logarithm so x=-25 is not a solution.
It's always important to know the rules of what's being dealt with before attempting it.
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