SOLUTION: If {{{ log(x, y^4) = m^3 }}} and {{{ log(y, x) = 4 / m^2 }}}, prove that m = 1.
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-> SOLUTION: If {{{ log(x, y^4) = m^3 }}} and {{{ log(y, x) = 4 / m^2 }}}, prove that m = 1.
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Question 1178302
:
If
and
, prove that m = 1.
Found 3 solutions by
Solver92311, MathLover1, greenestamps
:
Answer by
Solver92311(821)
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and
Therefore, if
Then
and
Eq 1:
Also if
Then
Eq 2:
Substituting the equivalent expression for
from Eq 2 into Eq 1:
Simplifying:
Therefore:
John
My calculator said it, I believe it, that settles it
From
I > Ø
Answer by
MathLover1(20850)
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If
and
, prove that
........change to base
...........eq.1
..........eq.2
if left sides of eq.1 and eq.2 are same, then
Answer by
greenestamps(13200)
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Note that the two equations involve
and
. Somewhere in working the problem you are going to want to use this property of logarithms:
Work with the first equation:
Now look at the second equation:
The two expressions for
must be equal:
