How do you solve 3log5x−log54=log516?
Answers
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0
Answer:
The answer is
x
=
4
Explanation:
To solve this equation you have to use the facts that:
a
⋅
log
b
(
c
)
=
log
b
(
c
a
)
log
a
(
b
)
−
log
a
(
c
)
=
log
a
(
b
c
)
First you use (1) to get:
log
5
(
x
3
)
−
log
5
(
4
)
=
log
5
(
16
)
Then you use (2) to get:
log
5
(
x
3
4
)
=
log
5
(
16
)
Now you can leave the logarithms (they both have the same base)
x
3
4
=
16
x
3
=
64
x
=
4
(because
4
3
=
4
⋅
4
⋅
4
=
64
)
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