Posted by **Adam** on Wednesday, March 20, 2013 at 10:22pm.

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 -
**Reiny**, Wednesday, March 20, 2013 at 10:53pm
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 -
**Adam**, Wednesday, March 20, 2013 at 11:22pm
fantastic, makes so much sense now, thx

- math -
**Adam**, Wednesday, March 20, 2013 at 11:25pm
and btw 3^2 = 25 is typo

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