Question 133420
find the value of log3 base 2 multiplied by log4 base 3 multiplied by log5 base 4 multiplied by log6 base 5 multiplied by log7 base 6 multiplied by log8 base 7. the answer is 3
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Rule: log(base a) b = [log b]/[log a]
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Your Problem:
[log3/log2]*[log4/log 3]*[log5/log4]*[log6/log5]*[log7/log6]*[log8/log7]
You see that a bunch of the numerators cancel with a bunch of the denominators
leaving you with log8/log2.
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This is true for any base, so let the base be "2".
Then you get [log(base2) 8 / log(base 2) 2] = 3/1 = 3
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Cheers,
Stan H.