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) (Show Source): You can put this solution on YOUR website!
\ =\ y\ \Leftrightarrow\ b^y\ =\ x)
and
\ =\ n\cdot\log_b(x))
Therefore, if
\ =\ m^3)
Then
\ =\ \frac{m^3}{4})
and
Eq 1: 
Also if
\ =\ \frac{4}{m^2})
Then
Eq 2: 
Substituting the equivalent expression for 
from Eq 2 into Eq 1:
^{\frac{m^3}{4}}\ =\ y)
Simplifying:
Therefore:
John
My calculator said it, I believe it, that settles it
From
I > Ø
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
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) (Show Source): You can put this solution on YOUR website!
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:
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