Question

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.

Answer 1

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

Answer 2

fantastic, makes so much sense now, thx

Answer 3

and btw 3^2 = 25 is typo