Posted by Alley on Saturday, April 6, 2013 at 8:50am.
Solve the equation
log(x+49) - log x=1
- solve the equation - MathMate, Saturday, April 6, 2013 at 9:26am
log14x+49 - log196x = 1
We will use a lemma that
Since 196=14², we write above as
log14x+49 - log14²x = 1
log14²(x+49)² - log14²x = 1
Rewrite using laws of logarithm:
log14²(x+49)²/x = 1
Using the alternate form from the definition of logarithms,
(x+49)^2/x = 14²
Transpose and solve for x to get
- solve the equation - typo - MathMate, Saturday, April 6, 2013 at 9:28am
We will use a lemma that states:
logax = loga²x²
The proof of the lemma is left to you as an exercise, if it was not already covered in your course.
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