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Hello,

Is log_3 (5) equal to log_5 (3)? Explain your answer. Do not evaluate the logarithms.

is my question. What is a surefire way to show this is false.

  • math -

    let x = log (base3) 5
    then 3^x = 5 , clearly x > 1 ,
    because 3^1 = 3 and 3^2 = 25 ,so x must be between 1 and 2

    let y = log(base5)^3
    then 5^y = 3 , clearly y < 1,
    because 5^0 = 1 and 5^1 = 5
    so y has to be between 0 and 1
    so x ≠ y
    and the two log expressions cannot be equal

  • math -

    fantastic, makes so much sense now, thx

  • math -

    and btw 3^2 = 25 is typo

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