SOLUTION: Solve without using calculator.
Which one is greater log3 to the base 2 or log5 to the base 3?
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Question 1107601: Solve without using calculator.
Which one is greater log3 to the base 2 or log5 to the base 3?
Found 3 solutions by Alan3354, math_helper, herosz:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Which one is greater log3 to the base 2 or log5 to the base 3?
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OR
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convert both to the same base:
From there you can use a calculator.
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A better solution:
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Ooops. That's not right.
Another tutor did it. You OK with that solution?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
In the 'better solution' given by another tutor, the answer comes out incorrect.
log(a) / log(b) does not equal log(a/b) because log(a/b) = log(a)-log(b).
I still don't have a non-calculator answer, maybe tomorrow, its late.
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Non-calculator solution:
Comparing vs is the same as comparing x and y in:
vs
Claim: x>3/2
Set x=3/2 to check:
Comparing the square of this to we get implying x > 3/2 (using 3/2 as the exponent gives a number that is slightly too small)
What if y = 3/2?
Comparing the square of this to we get implying y < 3/2 (using 3/2 as the exponent gives a number that is slightly too big)
We now have so we can say .
Therefore
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Answer by herosz(4) (Show Source): You can put this solution on YOUR website!
.
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